I imagine that most gay Republicans are attracted to the party because of their economic and or foreign policy stances, certainly not due to social issues, at least not related to homosexuality and the relationships of the party with the religious right.
More broadly speaking, there seems to be a battle ongoing over which faction will have control over the GOP. On the one side, we have mainline elements, closely affiliated with the Bush family, who are concerned with electability and holding power. Karl Rove recently started a new 501-4(c) corporation geared at making sure the party nominates "electable" Republicans for Senate races, as opposed to those financed by the hard right. On the other side, there's the Tea Party/John Bircher elements, which were held at bay for many years, up until Bush Jr. left office. In the wake of the financial crisis and the wider discrediting of the Bush wing of the party, they filled a vacuum. Ideologically, they share similar concerns, many espousing neoconservative ideas, but come from "different sides of the track", so to say.
The GOP crackup was probably inevitable. Inconsistencies and tensions within the GOP have been growing for years. The coalition that formed the modern GOP under Nixon and Ronald Reagan using cultural populism as a wedge is under some stress. Adding to this situation is Barack Obama, who is helping to fuel these divisions within the party to his advantage.
Republican libertarians have never gotten along with social conservatives, who want to impose their own morality on everyone else. Small government types in the GOP have never seen eye-to-eye with deficit hawks, who don't mind raising taxes as long as the extra revenues goes towards deficit reduction. The GOP's big business and Wall Street wing has never been comfortable with the nativists and racists in the Party who want to exclude immigrants and prevent minorities from getting ahead. Wall Street types like to use immigrants as cheap labor. And right-wing populists have never gotten along with big business and Wall Street, which love government as long as it gives them subsidies, tax benefits, and bailouts.
Sometimes these differences can be papered over by a national figure like Reagan or even George W. Bush at his political peak after 9/11 with nationalism and patriotic imagery that inspires the nativists and social conservatives. They gave big business and Wall Street massive military spending, and their anti-government rhetoric satisfied the GOP's libertarians and right-wing populists. Normally, maintaining this coalition intact required some sort of external enemy: terrorists, communists, etc. Internal foes included social liberalism and racial politics, at times veiled.
It all came to a heads in the 2012 electoral cycle: all the cracks and fissures of the GOP were exposed during that campaign. A clown-car full of candidates representing each respective wing of the party emerged: Bachmann, Perry, Gingrich, Cain, Santorum. Each rose rapidly as elements of the party coalesced around them, but fell once their major flaws emerged. In the background all along was Mitt Romney, a chameleon who appeared to be acceptable to all wings of the party, but ultimately, he ran an elitist, detached campaign that was also synthetic and inauthentic.
Even more troubling than these divisions is what the campaign exposed about neoconservative mythologies which have been allowed to fester. As a result, they've lost touch with political reality. This has given the Democrats the opening they need to aggravate tensions within the party. They're using the old Lee Atwater social wedge strategy against them. By emphasizing guns, they're pitting rural voters against suburbanites and urban voters. With abortion and contraception, they're emphasizing gaining a wider share of the woman vote. With immigration, the Democrats are looking to cement their hold on Hispanics, which gave GWB 44% of their vote in 2004.
Divide and rule seems to be the name of the game, only difference is that the Democrats are now using it to beat up the GOPer's.