They can ask/tell him to knock it off and, if he continues to make it a distraction, suspend him without pay. Then, if the NFLPA sticks it’s nose into it (Likely!), then cut him. Chances are, if they just cut him, it will divide the team further as some will consider it going overboard.
Cutting him would send a message though, wouldn’t it? Like the 2 assistant coaches that got fired.