I think I'd probably have put mouth-breather in the same category as window-licker: clearly insulting, intended to convey a disdain if not contempt for the target's lack of intelligence (no, stupidity), but probably intended as an insult to that individual rather than as a blanket condemnation or categorisation.
That said, it's a bit lacking in excellence, I wouldn't use it anyway, and if People Who Know regard it as disablist then I'm happy to go along with that.
Funnily enough, I don't have a problem with terms like moron, cretin or idiot, probably because I think they're now so far removed from their very specific historic definitions that they're now a mere insult.
Retard is, I think, far more offensive, while mong is clearly disablist (and derivatives like monging/monged out are too close not to be offensive, even though there is almost certainly no such intent from their users).
It is probable that I am sensitised to this last because my brother has Down's syndrome. Hey ho.