In most states, none. They can fire you for your haircut, your smile, whatever; they just can't fire you for something that it is illegal to fire you for.
I'm not talking about what an employer can legally do. I'm simply asking if it's stepping over the lines of decency and in some regard, a little bit of privacy.
I know the point can easily be made to go elsewhere if you don't think it's right, but what if all businesses started doing the same thing?