"there's no Constitutional right of freedom of expression when you're in uniform and working as a football player"

Free speech rights only apply to the government. The NFL could absolutely censor him and has censored many in the past. The NFL is doing the right thing in my opinion in this case but they certainly do not have to. The NFL should get credit for not stepping in here. They are making a conscious choice to allow this to continue I think it speaks well of the NFL that they are doing so, of course there is no way to tell how it would affect perception of them if they were to step in. It might be a calculated response.