It's all part and parcel, I think. Conservative Christians in the United States are used to feeling privileged, with respect to their persons and their ideas. They're used to being in power, and they hate the idea of not being able to force their beliefs on others, or at least to impose consequences for those who aren't in lockstep.
I don't know who's made more progress. Where I live now in rural Trump country, I would feel a lot more comfortable telling people I'm an atheist than telling them I'm gay.
Of course either is stigmatizing, and either would exclude me from any real possibility of public office.