Grout and joint compound could be kind of gritty in the washing machine pump and over time cause premature failure. Caulking and Loctite adhesive could stick to the wash tub and be a pain to get off. Latex paint should just wash away. If it were me, I'd just chuck the rags. I have a seemingly never-ending supply of worn out T-shirts to use as rags so I rarely wash them. They have been used and reused numerous times.