Japan
Japan has become one of the leaders in technology and innovation over the years. So, what does their history have to say about homosexuality. Well, quite a bit actually. It would appear that similar to Rome the most popular form of homosexuality was pederasty (the love between an adult and a younger man). The military and the clergy were where these acts typically happened. Older men would be mentors to younger men through a rite of passage that brought them to adulthood. Their relationship was founded on education, protection, love and respect, and ceased after the mentee came of age. These mentoring programs were prevalent in both Samurai and Buddhist monks. Pre-modern Japan was accepting and even encouraging of homosexuality and bisexuality. When we go back to 1,000 BC we find the establishment of Japan's first main religion Shintoism. Their first known texts, the Kojiki (Record of Ancient Matters) and the Nihon Shoki (The Chronicle of Japan), were completed in 712 AD and 720 AD. They relate to the creation myth of Japan and the Nihon Shoki records some of Japan's early history. There is nothing in either of these writings regarding homosexuality. However, it is interesting to note that the first three generations of deities described were all male. I will leave you to figure out the logistics to that one. However, there is no approval or condemnation of homosexuality in any of these texts. They held sex in high esteem, part of which is displayed in the Kojiki. The following is an excerpt explaining how the deities Izanagi and Izanami created the islands of Japan: 
At this time Izanagi-no-Mikoto asked his spouse Izanami-no-Mikoto, saying: "How is your body formed?" She replied, saying: "My body, formed though it be formed, has one place which is formed insufficiently." Then Izanagi-no-Mikoto said: "My body, formed though it be formed, has one place which is formed to excess. Therefore, I would like to take that place in my body which is formed to excess and insert it into that place in your body which is formed insufficiently, and thus give birth to the land. How would this be?" Izanami-no-Mikoto replied, saying: "That will be good."
It is interesting to note that in the creation story of Shinto sex was responsible for the birth of a nation and her people while in the Judeo-Christian religions, the acknowledgement of human sexuality and their banishment went hand in hand. Similar to the ancient Judeo-Christian religions in the West, Shintoism provided the basis for the belief system in Japan. As the religion evolved and was influenced by other groups and societies Shintoism still provided influence over the people. Shintoism was sex-positive, but there was a nagging concept of sexual "pollution" which Pflugfelder, author of Cartographies of desire: male–male sexuality in Japanese discourse, describes below:
While male-female coitus was seen as inherently defiling, obliging those (and in particular males) who had engaged in it to undergo purification before entering in the presence of the gods, Shinto authorities did not characterize male-male sexual practices this way, instead they showed far less preoccupation with the theological implications of such behavior than their European counterparts. No explicit condemnation of male-male sexuality appears in the Shinto canon, which in fact remains silent on the topic altogether.
Shintoism has a general message of "all sexual love being good." This helps to set the tone for Japan's second main religion, Buddhism. Buddhism was introduced to Japan in the 7th century. This was well over a thousand years after Shintoism. Traditional Buddhism viewed sex differently than Shintoism. In Buddhism, sex was linked to desire. In practice Buddhist were supposed to overcome this desire. Through overcoming these desires, one was able to gain enlightenment and escape from the cycle of death and rebirth. Buddhist monks and priests took a vow of celibacy in both heterosexual and homosexual activity. However, an interesting thing is that they believed heterosexual activity was of greater offence than homosexual activity. They considered women "evil and defiling" by nature. On the other hand, homosexual acts were treated as a "lapse in self-control." For example, there is a Vinaya (a regulatory framework for the monastic community of Buddhism) that was developed by Buddha himself:
At that time the venerable Upananda, of the Sakya tribe, had two novices, Kandaka and Makhaka; these committed sodomy with each other. The Bhikkus were annoyed…: "How can novices abandon themselves to such bad conduct?" They told this to the Blessed One… [who declared] "Let no one, O Bhikkus, ordain two novices. He who does is guilty of a dukkata offense." Gary Leupp, in Male Colors, The Construction of Homosexuality in Tokugawa Japan, explains: Here their sexual involvement is seen as the result of their environment; perhaps they share a cell with the monk who ordained them. Although their behavior is plainly regarded as "bad conduct," they are apparently not punished for it. Rather, the monk responsible for them is censured. 
Leupp continues: Only the holiest and most disciplined of Buddhist priests were thought capable of overcoming sexual desire and faithfully observing the Buddha's command to abjure all sexual activity. The rest of the clergy, it was widely assumed, would yield to temptation with male or female partners. 
Simply put, the act of male-male sex was simply a slap on the wrist. If we compare this line of thought with Judeo-Christian beliefs we see a stark difference. The Judeo-Christian has a hierarchy of "bad sex things" is completely opposite. Christian priests were also forbidden from partaking in heterosexual activity. However, male-male sex was considered a crime and the punishment would be severe. While the Judeo-Christians held the belief that ascension to heaven was a one-time shot, for Buddhist ascension to nirvana was more a journey so if they couldn't figure out celibacy in this lifetime, they still had the next one. It is important to keep in mind that this is Japanese Buddhism. Some Indian and Chinese Buddhist sects had a more radical different idea in regards to the nature of sex and homosexual relationships. The only actual rule that can be found in Japanese Buddhism in regards to sex can be found in the "five training principles" of Buddhism. However, the wording is a bit vague: "I take the rule of training not to go the wrong way for sexual pleasure. Dharmachari Jñanavira, author of Homosexuality in the Japanese Buddhist Tradition, speaks of the golden mean: "the deed which causes remorse afterward and results in weeping is ill-done. The deed which causes no remorse afterwards and results in joy and happiness is well done. 
After a century or two Japanese Buddhism began developing its own sexual identity. The Tachikawa-ryu branch of Shingon Buddhism which was latter known as "the main sex cult of Japan" has a Tantra that includes the idea that sex would help inspire an individual toward enlightenment. The Tachikawa-ryu Buddhists not only seen sex as a religious symbol, but as a good thing in general even if procreation was not the desired result. 
As Jñanavira puts it:
Although present, Tantric sexual imagery which involved the unification of male and female was of marginal influence in Japan. Far more pervasive in male Buddhist institutions was the influence of homoerotic and even homosexual imagery where beautiful acolytes were understood to embody the feminine principle. The degree to which Buddhism tolerated same-sex sexual activity even among its ordained practitioners is clear from the popular myth that the founder of the Shingon school, Kooboo Daishi (Kuukai), introduced homosexual acts upon his return from study in China in the early ninth century. This myth was so well known that even the Portuguese traveler, Gaspar Vilela had heard it. Writing in 1571, he complains of the addiction of the monks of Mt. Hiei to "sodomy", and attributes its introduction to Japan to Kuukai, the founder of Koyasan, the Shingon headquarters. Jesuit records of the Catholic mission to Japan are full of rants about the ubiquity of pederastic passion among the Buddhist clergy. What particularly riled the missionaries was the widespread acceptance these practices met with among the general populace.
In the nanshoku tradition, an older Buddhist monk called the nenja would take on a prepubescent boy, called the chigo, as his acolyte. Both the nenja and the chigo were expected to take this relationship very seriously. Some nenja would have to draw up vows of commitment. When the chigo reached adulthood, the nanshoku relationship ended and the nenja would then be free to seek another chigo. This kind of homosexual (child molestation) act happened in very specific circumstances between an adult man and an adolescent youth in the few years before he reaches manhood. Upon coming of age, any sexual element to the relationship is let go and the bond continues as a close spiritual friendship which is considered to continue beyond the confines of the present life. Homosexuality in adults was not the result of nanshoku. The acceptance of homosexuality in Japan was tied to their lack of care from the general public toward the practice. 
By the twelfth century, samurai had become the ruling class of Japan. Their numbers swelled from an initial 6,000 samurai in 1,200 AD to hundreds of thousands just a few centuries later. The samurai respected Buddhism and their sons were sent to monasteries to receive their education and inevitably enter into a nanshoki with an older monk. This practice became normal and even optimal with several generations of samurai. Pre-1600s during what is considered the warring states period, samurai were out fighting for long periods of time. There were no women around on these long journeys. When peace came during the Edo Era (post-1603), samurai were required to leave their home villages and live in castle cities in order to govern and prevent rebellion. So, once again you have an abundance of men and little to no women. The samurai eventually brought nanshoku out of the monasteries and into their cities. This version was referred to as wakashudō. Similar to nanshoku prepubescent boys would be apprenticed to an older man. Now, he was expected to learn martial arts, life skills, and, if the boy agreed, be the man's lover until he became an adult. This was formalized as a "brotherhood contract," according to Leupp. It was considered to be an exclusive relationship, though many a drama is known to have come about due to the cheating of one party on the other. Over the years there was much discussion in regards to Male-Male sex and Male-Female sex. In 1640 we see the Denbu Monogatari (The Boor's Tale). In it, men are bathing in a river to escape the heat. They begin to debate whether the love of a boy or a woman is better. In the end (SPOILERS) the woman-loving side wins, but not before conceding that "male-male erotic pursuits are well suited to the higher circles of the warrior aristocracy".
On the topic of homosexuality vs heterosexuality, it would appear that neither had anything to do with each other. Neither one was considered "more acceptable". They determined that simply preferring one over the other doesn't mean the other is invalid. They also believed that even if you prefer one over gender over the other (heterosexual or homosexual) you could still participate with the other gender if you wanted to (bisexual). The point being if you want to do something then do it and you should not treat someone else harshly simply because he or she chooses to do the opposite. 
Around the 1600s all samurai were required to move to castle cities which brought a large influx in people including a need for infrastructure and labor. Peasants migrated to these cities in order to fulfill this demand. For the first time we see a lot of interaction between the samurai and common people. This exposed them to the ideas of nanshoku and wakashudō. Wakashudō was seen as a high-class thing to do. Naturally non-samurai began emulating this behavior in big cities. In the lowest class this began with merchants because their wealth allowed them to acquire servant boys and apprentices. Not everyone could afford such an arraignment though. This led to the development of male prostitutes. This allowed for anyone to simply pay for either heterosexual or homosexual sex. Japan eventually entered into a period of peace which led to a growth of the middle class and made the samurai class poorer. Their chigo became another mouth to feed and it became easier to rent a prostitute then continue with the previous tradition. Street prostitution became big brothels and they even found their way into theaters. Many of the amateur kabuki actors were simply male prostitutes in disguise and when they were not on stage they were in bed with paying admirers. As male-male love became mainstream and accessible, wakashudō became less and less relevant. The partners became older too. As long as the men retained a "youthful appearance", they could remain prostitutes into their twenties and thirties. It did not last forever though. By the mid-1700's there was a lot of crackdown by government officials on the prostitution trade. As the crackdowns were put in place and more women began to come into the cities, male-male sexual activity began to decline. In 1859, Japan opened its ports to foreigners and with that they brought their severe hatred for homosexuality of any form. Naturally, the westerners were appalled by their acceptance of homosexuality and in order to be "modern or normal" and obtain a relationship with these foreigners they adopted stricter laws and before long homosexuality was a bad thing. (Kiochi, 2015)