Doing a cursory read of the relevant Wikipedia article
https://en.wikipedia.org/wiki/History_of_homosexuality (excuse me for my laziness), it seems like homosexuality gradually became more acceptable starting around the end of the 18th century, although the biggest change happened from the 1970s onward. So one could argue that the gradual increase in the acceptability of homosexuality mirrors the decline of modern culture, but I think that it actually predates the decline of modern culture (assuming, as you argued in another post, that modern culture started declining toward the end of the 19th century). Also, homosexuality was acceptable in many other cultures during their peak, such as in ancient Greece and Rome, and even in medieval Islamic cultures. Therefore, I would argue that there is no correlation between homosexuality and declining civilizations.
Also, just out of curiosity, what are your thoughts on birth control and abortion? One could argue that they are bad because they encourage premarital sex, but I think that cultural values have a greater effect on whether people have premarital sex or not. And if birth control was not available, then overpopulation would become an even greater problem.