The Log Cabin Republicans are standing behind Trump, party before all else.
The USA being a large country. Every demographic group has a lot of Trump supporters in it, even if they're a small minority within that group. Trump's worst demographic in 2016 was black women, and there were probably still a hundred thousand black women who voted for him.
It's entirely possible to endorse a political party that wants to strip you of your rights or even kill you. It's especially possible if you're the kind of person who isn't deeply reliant on those rights, or who has the money to ignore what you're losing. For example: Peter Thiel is rich enough that there's no realistic way his sexuality will really matter to him; if things get bad enough, as they might, he can load up a private jet and skip town.
It's easy enough to think that the Leopards Eating People's Faces Party is only going to feed other people to the Leopards. Some people are single issue voters and that issue doesn’t have to align with a demographic group. If you are LGBTQ and either anti-abortion or anti-immigrant, Trump is pretty much your only candidate.
Hey!..lol. He's Made America Great Again, boosted the economy (DOW over 25000!!) , solved the North Korea problem once and for all, turned the screws on China and rebuilt American manufacturing to its former glory, and generally pissed off the libs on an almost daily basis!
If the LGBTQ+ community can't appreciate all of that, that's their problem.