I have always wondered if the pendulum is really about sexuality at all. It could be that we just become more or less authoritarian. And certain groups are just a victim of that swing.
Many of the traits in society or identity that we believe to be static (especially when viewed from outside) or axiomatic turn out to be more complex and more fluid than they initially seem.
So there is this one data point of correlation.
Stupid as it is, anti-gay extremists do make that argument, that the cultural acceptance of homosexuality is a slippery slope towards the eventual normalization of pedophilia and even bestiality. That can be seen as an argument pro Christian authoritarianism of a specific political bent.
But looks like you and X other people can't read and feel very defensive about something that no one has actually said.