A centrist on gay rights likely sees that marriage is legal, culturally it’s acceptable, so why should they fight for more rights, they’re already equal?
But they factually aren't equal. It's legal to discriminate against gays in a variety of ways -- including in employment and, apparently, when selling business services. They are not a protected class in most places. They are directly targeted by hostile, criminalizing legislation all over the place. They aren't fighting for MORE rights, they're still fighting for equal rights and are far, far away from winning them.
Which means the centrist position, by your logic, is that gays should remain second-class citizens because they already got everything they need, even though it's still factually legal to discriminate against them? That's not actually different from the far right's position that it should be illegal to be gay. It's far, far away from the liberal position that people have a right to not be discriminated against. There's no moderation in that position. It's still the "kill some gays" position.
So no, I'm not incorrectly simplifying. I'm cutting away the bullshit. If you or anyone you know is a "centrist" on gay rights by the logic that they "already" are safe, those people are monsters. The only way to be a "centrist" in the way you have described is to be upsettingly ignorant. And if the entire philosophy of centrism is that these people are too ignorant to form a cognizant moral position, what are we even talking about?