That a good point. If you can prove to a court the government was involved in the creation of the limiting policy, you may have something. I think it would be tough to prove though but I like the way you think. Thank you for pointing that out.
FYI: I dont think they are the same. Barnette vs Virginia was about a state mandated action. The state cannot infringe upon a persons1st amendment rights. The NFL policy is an employer mandated policy. Just my humble opinion.