This is only an opinion derived from my own empirical experience, but I think many (social) conservatives are not bigoted (or homophobic, in this instance) per se. More specifically, they are not driven by hatred or intolerance, but by indifference.
This the same way I feel about the “Is George Bush racist?” debate. I don’t think George Bush hates black people, or gay people - but his insulated, pampered lifestyle afforded him the luxury of never having to think about it.
Many conservative people I know are like this. They throw out flippant phrases that could be seen as bigoted or racist when the occasion presents itself, but it’s really not a relevant aspect of their lives. In other words, they don’t tend to take any racist or bigoted actions unless they are prodded to do so via other, perceived personal (i.e., selfish) interests.
So to answer the OP: The conservative outrage is not there because the conservative propaganda has not prodded them into caring by providing a reason. And left-wing “reasons” don’t enter into it at all - they have already been indoctrinated to discount anything coming from “the left”.
Another possible factor is the general “anti-sexuality” bias coddled by conservative propaganda. Conservatives are indoctrinated with the idea that any sexuality not sanctioned by religion or marriage is to be avoided at all costs. So it really doesn’t matter who Gannon might want to have sex with (or the more relevant issue of his self-hating rhetoric against homosexuality) - all sex outside marriage is wrong, and we know how common that is (thanks to liberalism, no doubt) so what’s the difference here?
Remember that the legal initiatives are against gay marriage, which does nothing to abate the levels of gay sex outside marriage. And of course, we know that will continue, but the most important thing is to keep up appearances. This (getting caught) is Gannon’s biggest sin, but it’s not an unforgivable sin according to the conservative propaganda. People can always see the light, and be absolved of past transgressions, either religiously, or politically.
I believe this is the thinking. And it is political gold, because it encourages intolerance and hypocracy, and forgives them at the same time.
And finally, as you’ve admitted yourself, Gannon’s sexuality (apart from the self-hating rhetoric) has nothing to do with why it was an outrage that he was given access to the WH press corps.
IMO, by looking for conservative “outrage” on the basis of his sexuality, you are giving your conservative critics here the means for avoiding the real issue, and pointing the finger of intolerance back at you. Why do that?