Axiom 29. The enemy of my enemy is my enemy's enemy. No more. No less.
I'm in a different country, so the absorbed norms are different. Gays seem to be found through all aspects of the political spectrum here, and can range from totally anti-gun to pro.
A number of years ago I was involved in preventing a State take over and closure of a major federally owned shooting complex. The State Premier (Governor) was generally accepted to be a closeted gay and was very anti-gun.
The State opposition leader from the other party expended political capital so I could meet with the Federal Minister responsible and block the move.
That opposition leader voted against his own party to lower the age of consent for homosexual acts, the party member who acted as go-between for us was a proctologist with vanity tags 'AssDr'.
Reading between the lines, both sides of the political spectrum had homosexual or, at a minimum, pro-homosexual individuals at the top.
Their sexual orientation didn't matter on the issue of guns. Nor, really, did their politics, as the opposition leader was from the same party as the Prime Minister who banned semi-autos. What mattered was their interest, or lack of it, in individual liberty.
One of my gay clients was a great classical musician, I kept one of his CDs in my car for years. He was opposed to gay marriage, because marriage is for straights to have children. He was also opposed to the demeaning treatment of boys at 'parties' held by the law partner of another conservative State Premier.
A shooter I know is Jewish, gay and has a mother complex out of New York via Hollywood. He's also a successful businessman and conservative.
Another is an excellent long range shooter and runs multiple 'bath houses'. Zero interest in politics, guns are his bling.
Another, a Colonel in the army, apolitical, his homosexuality was a non issue for him, as it was outside of his duties. Until he was harassed by his superior and submitted his resignation out of principal. His medical skill set was considered essential, so he was promoted above his former superior.
Why the anecdotes?
Because I don't hold with the idea that there is a 'BLT&M' community. There are simply people, some of which share common interests. The lesbians I have known didn't care for homosexual men, the homosexual men didn't have much to do with lesbians and thought transgender people were seriously confused. The only shared characteristic was frequenting the same pubs, which tended to have been the ones that accepted them in more oppressive days. Politically they were across the spectrum of the parties and their attitudes ranged the gamut of liberal, libertine, libertarian,conservative and communist.
Sexuality is only a minor part of a persons character. It doesn't define their all, unless they obsess about it. Those that obsess about it are not going to care about RKBA, other than how it impacts them and their obsession. Those that live a broader life? They may be open to our arguments, or already share them.
I see zero need to play along with Social Justice Warrior 'Shut Up, Because Reasons' games, they are played by the obsessed. The intention is to negate any viewpoint other than their own, twisting the conventions of polite society to their agenda and close down communication by those other than them. Orwell warned against the redefinition of words to control thought processes. No one has a right to not be offended.
On the other hand, the exact opposite is required to improve the position of RKBA, we need considered discourse. People in fear will not support RKBA for others, arms makes the Other even scarier. Angry people are destructive and will see being armed as a means to that end. Rational discussion requires at least a modicum of respect for the other person for communication to take place. If you want to promote shooting to a gay person, treat them as a normal human being and invite them shooting. To be deliberately offensive is bad manners and non sequitur. The subject is RKBA and the shooting sports, not gay marriage or the theological rights and wrongs of the gay life style. It's possible to disagree on those subjects and find common ground elsewhere.
I expect groups like the Pink Pistols and activists like Tom Palmer will continue to do what they do, regardless of any opposition they see from some shooters based on how they live their lives. They have made a considered decision to promote civil rights. That includes the rights of people who don't like them and people they don't like.
But for the average person? Polite acceptance that they are a human being and not a stereotype goes a long way.