The history of homosexuality in the world is very much a complicated matter. While sexual orientation is a modern idea, the stigma around particular homosexual relations is not. In Ancient Greece, for example, relationships were based around cultivating masculinity. For example, sexual relationships between men and boys were tolerated because according to Greek tradition, to have a relationship with an adult was a sign of becoming a man. But in an purely adult relationship, if one member of the duo took on a passive role, then that passive member of the relationship would be scorned. Homosexuality was rife within the Greek military, because it was believed that if the men of a unit cared about each other, then it would reinforce morale.
There is no specific point where homophobia began, but there is no specific point where widespread tolerance for it began either. Different cultures had different beliefs surrounding the practice of same-sex relations. It definitely didn't start with Christianity, as Zoroastrianism also took a dim view of homosexuality. In China, the issue of homosexual relationships varied widely, depending on who you asked. Ming Dynasty literature celebrated homosexual relations while some people viewed Confucianism as being homophobic, due to listing not having children as sin against filial piety. Some emperors even had male concubines.
Several ancient dynasties in China also took a dim view of homosexuality, though there is debate as to when this dim view took root. Some say it began in the Tang Dynasty, which was influenced on some level by Christian and Islamic values, though some say such attitudes go back earlier to the Song Dynasty, which forbade male sex in the course of prostitution, though the first blatantly homophobic law came into effect during the Ming Dynasty. However, from my research, homosexuality and discussion of it is tolerated within the People's Republic of China, with it becoming a popular topic on Sina Weiblo after the legalization of same-sex marriage in the USA, though this liberalization only began in the 1980s, with Mao Zedong voicing his support for castrating 'sexual deviants'.
My point is, there is no simple POD I can list in which homophobia is neutralized. I can also not say that tolerance of homosexuality is a modern idea, since again, different cultures had different ideas. The only reason why homophobia is a issue now is because a singular religion has imposed itself in the West and integrated it's beliefs on sexual behaviour into the laws of several notable nations and the beliefs of high-profile individuals, who have had a reach unseen before thanks to the Internet.