They will then counter this with "Well if they just shut up and minded their own business instead of telling everybody all about how much cock they suck, it wouldn't matter", completely missing the point that these folks have been minding their own business for centuries and regularly getting murdered for it, and also completely missing the extremely obvious parallels to Jim Crow and the civil rights movement (or maybe not, maybe that's why they hate it so much). It is their opinion that they shouldn't have to know you're gay, and that you should have to live in fear of revealing that fact for your entire lifetime. And that's just the crowd that doesn't believe that homosexuality is a direct affront to God and should be stamped out as a moral imperative.
I've had this conversation before a few times, it always comes back around to the same points. Conservatives become extremely unconformable with the knowledge that The Gays(R) exist and typically wield misunderstood Bible quotation in defense of that. Those who don't, will resort to the argument that they shouldn't have to have it "thrust into their faces", as though the knowledge that gay folks exist is some great personal burden to them. They will happily tell people to "mind their own business" and "keep it to yourself" so long as their lungs have air with which to speak, but when told themselves to mind their own damn business, suddenly this is unacceptable.