The distraction and/or division. You don't want guys from any political persuasion dividing your teams and fans attention away from beating the next team you face.
You don't want guys answering questions during the week to whatever the latest controversy is. This sort of stuff can also rub players the wrong way. "They're talking about our idiot QB instead of my 3 TD's against the best defense."
Usually also these guys are a bit high strung, make dumb penalties, and tear apart a locker room. Even ones where they agree. Just look at Seattle. They have had a few morons on their team, and now they're imploding, partially from that.
We want people who live, breath, eat football. It's alright to have causes, but don't be controversial or take the focus away from the teams goals.
You don't live, breath, eat football if you're making a spectacle about yourself.