Over the last two decades and more, the Republican party has tended to play the anti-gay card whenever it suited it either directly, or by avoiding anything that might infuriate the anti-gay lobby. In fact, the studied neglect of the AIDs epidemic during Reagan's watch more or less precisely coincided with the period during which it was assumed by the mass media that the epidemic was confined to gay men and drug users - leading Republicans explicitly regarded it as God or nature biting back.
The triumph of the Republicans in the mid-term elections of the first Clinton term was linked to the preparedness of smart right-wingers like Gingrich and his libertarian allies to make a pact with the Moral Majority. Political victory was worth pretending that you would consider their agenda. Opposing gay rights, banning the teaching of evolution and restriction of abortion were all issues that e.g. Gingrich was far too bright to actually be enthusiastic for - but he and his made the calculation that it was worth it.
Gay Republicans like Sullivan wanted marriage rights as a way of buying in to normality and hey! this is not especially a bad thing. And they won the argument with large parts of the LGBT community, but not with their political base. In the end, GW Bush has kicked them in the teeth.
Let us be clear. I am not gloating. But honestly, LGBT Republicans might have considered the probable consequences of their party's alliances? Turkeys should never vote for Christmas. And, however much they dislike what they call liberals, at least liberals are not cosied up to people who would stick us all in concentration camps, or stone us to death in the street.