As for your first contention, there is a compelling state interest in having sporting events with huge audiences be conducted peaceably, so it’s a legitimate case for extra police protection, commensurate with the potential hazard of disorder.
If it’s off-duty moonlighting, that may be an out. It’s the owner who specifically wants police personnel as a deterrent, rather than mall cops and Pinkertons. But arguments can be made that the sheriffs, while off-duty, are using the prestige of their office to get this particular job. I don’t know if that’s relevant or not, though.
There is actually case law on the departments’ side in both cases. It’s especially in a case where the police are providing special escorts to the players. There is a case to be made that the police need to secure the stadium and the masses inside - there is precedent that the police can stop the special escorts and still be legally providing equal protection.
Well, if we’re talking duty/contractual obligation, last I knew official NFL policy dictates that players be on the field for the anthem, stand at attention with the helmet tucked under one arm. Has that policy changed? If so, when, why, and by whom? If not, what’s with the personal choice cr@p??