So, recently my wife's boyfriend has finally taken the big

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So, recently my wife's boyfriend has finally taken the big step and moved in our house. I have been very dubious about this snce the guy in question has basically been evicted from his small apt for being loud and has already a pending subpoena, but my wife eventually convinced me, and so here we are.

The point is, since day one our house is a perennial mess. He refuses to do the dishes, to clean or to contribute to the house in any way, he just has sex with my wife whenever he wants and has no respect for my property or my money. I would like him to stop, but i understand that the issue is potentially sensitive since he is black. I would like him to cooperate, but i'm also scared of appearing racist (i'm clearly not, my wife's son is half black himself, tho different father, and i have never mentioned the thing).

Is there a sensible way to put an end to this and maybe find out a way for him to behave without upsetting my wife?