To answer you straight up. NO they can not wear anything else, ever.
Imagine Jordan going to the store in reeboks. The media would kill him. Reebok would turn around and use it for promotion like "look what he really wears" and Nike would have a PR nightmare.
So in contracts it tells you what you can and can't wear. Say you sign with Nike. They'll tell you, you can wear products we don't sell. Or maybe new era hats. Suits. Dress shoes. Certain watches and shyt.
But more than likely, they'll tell you, it better be Nike. Like shirts, hats, socks, shoes. But then again, you signing 30 mil deal with Nike, they also give you all that shyt first and free. I remember in MJ's book he said he would only wear a pair of J's in 2 games before he didn't like the feel and then he'd just get overnighted some more
Now your friends and fam, they didn't sign any contract so they can wear whatever
shyt I remember when making the bond films, they told pierce bronson he couldn't wear a tuxedo in another movie for like 3 years. They can make you do anything in a contract. As long as you sign your name