Sadly, the bacteria is going to be there regardless of whether it's "outside" or "inside" clothes. I personally wouldn't be upset unless he's tracking actual dirt or grime into the house, but that's me. If this is a hill you're willing to die on so to speak, explain to him how much it means to you and see if you guys can't find some kind of agreement. Be reasonable and clear about your expectations and also listen to his side of things. Surely you both can work it out.