If, on the other hand, you mean suddenly dropping over for tea and scones of a weekend morning, or fruity pink drinks after work, then no, I don't think they're obligated to "suck it up". Their neighborhood, from their perspective, has just been "invaded", and they have a legitimate right to feel aggrieved by that, right or wrong, bigotry or not, assholery or otherwise.
Just like the folks in Lincoln Heights have a right to feel aggrieved by Rhinehart's ugly, unmaintained container — except, of course, that the gay couple didn't break any laws. (Just a few years ago, they might have, depending on jurisdiction, but since Lawrence v. Texas, there isn't even that; it's just confrontational, and possibly even rude.)
I'm also doubtful that the gay couple truly hasn't broken any laws. I'm sure that with enough digging, the homophobic neighbors can find a fence on the wrong side of the property line, a deck that isn't zoned properly, or something similar; the neighbors could even pass a HOA regulation prohibiting pride flags. Does that make it morally justified, because it's "their" homophobic town? It seems like you think so.
Would you call it confrontational for a KKK member to move into a black neighborhood and fly Ol' Dixie? Because that's perfectly parallel to your proposed scenario, and that's what you're arguing for.
Just because the people we're talking about are members of a protected class doesn't change the logic of the situation.
Do you legitimately think that's not thumbing their noses at their new neighbors? Do you actually believe that the neighbors – you know, the folks who were there first — have no choice but to suck it up? "Welp, they bought the house and moved in. Nothing to be done about it now."