I don't think Dog ever decides to leave you, though I've never tested this definitively and could be wrong. If his reaction falls to hatred (or perhaps even dislike) he might run off... or even turn around and bite the hand that feeds him.

Other followers can usually be mollified with specific items (dwarven snuff, brandy, wine, elven spring water, etc.) but a few such as Chukka are one and done. Though I think this applies more toward acts and quests which go against their declared alignment, and less toward negative reactions brought about by clothing.

I actually think you may be the first to discover where the threshold lies; or at least, become the first to publish the results.