"...do you suppose the gays think there is a radical religious agenda of suppression and exclusion?"
If homosexuals think that there is a radical religious agenda of suppression and exclusion, that is evidence that they are seriously incapable of rational thought, know nothing of history, don't understand hygiene, the spread of illness, the inherent dangers of same sex sodomy and promiscuity, and are focused solely on their sexual proclivities to the exclusion of everything and everyone else.
If someone actually thinks that, he or she is actually very mentally ill. To have as the entire focus of one's life the method whereby one achieves orgasm (and a very nasty way at that) and to view everything in the world through the lens of that method of achieving orgasm, is utterly selfish, miserable, and by its very nature, the narrowest and most exclusionist of viewpoints.
Answer: A large majority do, but there are a few quasi-sane ones who don't. When I was still lost in my homosexuality, I was reading a lot of homosexual literature, especially the so-called "gay Christian" (Google it and see) stuff. I noticed that nearly every one of the resources took potshots at "fundies" and the "religious right," so much so that I know a former conservative who went to those sites and now thinks that we're modern-day Pharisees. My second former boyfriend, who still is a proclaimed conservative, has grown an irrational hatred for all believers who think that homosexuality is a sin. That's how "infective" the resources are.
Yes, there are a few homosexuals out there who just want to be left alone, but they are vastly overwhelmed by the radicals. It's almost impossible to read and accept the majority of the literature without becoming a radical. It's rather ironic that they preach love, tolerance, and acceptance while loudly denouncing Christians, etc. Those who aren't the radicals are frequently denounced for being self-hating gays and are intimidated much like straight people are. And ex-gays are viewed as traitors and objects of alternating ridicule, pity, and hatred.