According to John Boswell, the 13th and 14th centuries saw growing intolerance against minorities in general, including Jews, heretics, 'witches' and gay people - which he links to a desire for uniformity as nation states were emerging.

And during the High Middle Ages the reasons for condemning homosexuality shift from a combination of 'debased animal behavior' and 'unnatural behavior' to the latter, maybe because growing urbanization made intellectuals unaware of homosexual behavior among animals.

Source: Christianity, Social Tolerance, and Homosexuality (1980). This is a controversial book with regard to the existence of same-sex unions in early Christianity, but Boswell did read many primary texts in the original language.

There's also a theory that homophobia grew when Pope Gregory VII declared celibacy compulsory for priests in the 11th century. That amounted to a ban on heterosexual marriage, while gay affairs went under the radar, and critics forced the clergy to defend themselves against accusations of 'sodomy'. I don't remember where I read this theory; it might have been Boswell, too.