I can understand why the teams don't want their name to be taken advantage of in this way by the players. They have a brand to protect.
So this is an interesting example of how different rights conflict: the NFL's and the team owners' IP rights versus the players' speech rights.
It seems to me it isn't as simple a conversation as a first amendment right being trampled by malevolent owners. They have an interest in the value of the entertainment they provide.
Many people watch sports as a means to set aside politics in favour of watching thugs beating one another up.
Wait. What? It's the same thing as politics in a different coloured outfit.