I would not entertain a single thought about allowing them in my home.
They are on a scouting trip:"See something, say something." Your two gun collection , and 50 rds of ammo will be reported as an arsenal. You'll get red-flagged in half an hour after dinner, when his screaming bitch companion decides he's been threatened. They are going to expect to have sex under your roof. They are going to push their "business" into everybody's faces who live there. And you are "supposed" to accept all that bullshit.
Tell them you got the double covid, or will be in Ukraine, or "I'm expecting to be sick then, so please stay home".
At the absolute LEAST level of offensiveness, he is seeking validation, because his closer family has told them to take their mental illness and depravity elsewhere. He chose you.
Would you allow someone in your house to screw your daughter. Noisily? Would you share your wife? Would you say nothing if a guest decided to take a crap in front of the hearth? Fart unrepressedly? Screw with the Thermostat? This guy is a near stranger, would you allow that with anybody else you have only seen 4 times in a lifetime?