I’m not gay, so I’ll offer an analogy. I’m a brown guy with a beard from a Muslim country and with a Muslim last name. I found my friends’ (sincere) concern about Trump’s campaign rhetoric to be odd, because I didn’t find it alarming myself. (Apparently 30% of Muslims polled did not.) I thought it was distasteful and counterproductive—pissing away a demographic George W. Bush won in 2000–but I felt all the rhetoric on the left about concentration camps was way overblown. I didn’t support Trump for other reasons, but the mere presence of some xenophobes in the party wouldn’t keep me out of it. I care about my safety, but I don’t really care if other people think we should have fewer Muslim immigrants. (Also, being from a Muslim country I know that the security issues aren’t totally manufactured.)

Now, what do you mean by “erase?” Republicans don’t want to put gay people in concentration camps and forcibly re-educate them. But it has taken them longer to come around to accepting gay people than Democrats for predictable reasons that gay Republicans are presumably willing to put up with. Conservatism by its nature values the traditional family because they believe it is beneficial for society. The long-standing belief that being gay was a “lifestyle” along with 1970s rhetoric about disrupting the traditional family was predictably alarming. For liberals who had already abandoned the idea that society as a whole should pressure people to get married and have 2.1 kids, acceptance of same-sex relationships that wouldn’t necessarily follow the traditional path came much more easily. But attitudes towards same-sex relationships and marriage have evolved rapidly even among conservatives. In 1978, few people accepted that being gay was genetic. Today, 50% believe that. Acceptance of gay marriage very closely tracks rising understanding that being gay is innate. (Republicans aren’t as far along as Democrats in internalizing that. But even among Democrats only 61% believe that being gay is fully innate, so it’s not like gay Democrats can get totally away from such beliefs either: https://news.gallup.com/poll/234941/say-nature-nurture-expla....) Moreover, in this past decade studies have revealed that huge percentages of gay couples are already raising kids together. In the last decade, an image of gay people as being born that way, and being in committed relationships and raising kids no different than anyone else, has appeared. And it has enabled the reconciliation of conservatism and same-sex relationships to the point that half of Republicans already support same-sex marriage.

Gay Republicans presumably understand this thought process and are willing to work through it and let the process play out.
Many, even agree with the general principle of social conservatism, even if they disagree about the specific case. It’s worth noting that gay conservatives played an important role in Obergefell. See: https://slate.com/news-and-politics/2015/06/gay-marriage-vot...

> In 1989, most Americans had never even heard of gay marriage, and certainly couldn’t conceive that it would one day be legalized by popular vote. That year, Andrew Sullivan wrote a landmark essay for the New Republic, “Here Comes the Groom: A (Conservative) Case for Gay Marriage.” Sullivan’s essay is one of the most important magazine articles of recent decades. His argument, which he went on to elaborate in his books Virtually Normal and Same-Sex Marriage and in later essays, is that marriage for gays would “foster social cohesion, emotional security, and economic prudence.” Sullivan’s conservative case would eventually become the intellectual and moral foundation of the campaigns to legalize gay marriage. Sullivan gave Slate permission to reprint his New Republic essay in full.