A few people seem to be over-reacting.

There are strangers in your home. Would you leave the house with no bra? If not, then put one on when strangers are in your home.

If you want to walk around your home with no bra and strangers are looking at you, then that's on you.

Also, it's your mother's house. If you're going to live there and she wants you to wear a bra when there are men you don't know in your house, then put the bra on. You can be braless as much as you want with whoever you like when you're paying for your own house.