Yes, they're a medieval religion. My point was in comparison to their contemporaries, not in comparison to the modern day. Everything is relative.
That's shifting goalposts. You explicitly said that homophobia is not part of the Faith. You were shown that it is not just cultural attitudes, but that the Church is actively speaking out against same sex relations. And while you may have a point that misogyny was widespread in history across several cultural spheres, homophobia is more specific - that is not just "being medieval", that is indeed specifically the Faith. Given that, what we are will always be an abomination to the Faith, and we hence have an additional interest in keeping it small and marginalized. Defanged, as Maegor achieved - that is a good state of affairs to have.
This goes even
if it were "just customs" - you cannot separate social religion from social customs. Majority religions will always be about what is culturally ingrained in a society, even in preference to scripture (not that all religions have those). Thus, the main defenders of old tradition and social customs will always be the Church, or whatever else religion there is. And yes, that would go for the Old Gods as well, but they don't even have any organized religion or even just disorganized clergy to begin with, so they are not really a factor.
The "cool magic stuff" is locked behind either burning people (R'hllor) or eating people (Old Gods) in ASOIAF. The good thing about the Fot7 is that compared to the other religions of the setting it is the one that doesn't practice human sacrifice. And even if we were cool with that, we did not pick scholar.
While both the Old Gods and of course R'hollor
have human sacrifices, the notion that magic is "locked behind" those is clearly not true. Stuff like greensight and warging is clearly associated with the whole complex of the First Men/North/Old Gods, and requires no human sacrifices. We have several instances of woods witches and the like, and while their magic repertoire could include human sacrifice, it clearly is not obligate for every bit of magic or foreseeing they are doing.
Edit: Calling Cersei getting her comeuppance as a warning against the Faith getting too powerful seems kinda ridiculous to me? Like yeah, they're right? She obviously did practice incest and commit regicide. She had it coming. That was not some kind of witch hunt.
That's such a weird way to look upon things in the context of what to do with the Faith. "Comeuppance"? I mean, obviously we have a vested interest in that
nobody should be able to judge us, "comeuppance" or not. As I have said, we want the Church small, docile and defanged, so they will not be able to judge the Queen of Westeros
at all Because, uh, we're gonna be that Queen, so logically that is in our interests. Luckily, the Church is already destroyed as a centre of power, thanks to Maegor, and let's keep it that way.