From what I understand, the military pays the NFL a certain amount of money to promote them, so they're kind of like a sponsor.
I agree people constitutionally probably can't be forced to stand for the national anthem, even though it is a business. IMO it's bad business to offend customers by disrespecting the flag (and a lot of people take it as disrespecting the flag, no matter what people say). So I agree the best thing to do would be to simply stop playing the anthem. The anthem is meant to unite people, and clearly it doesn't serve that function anymore. The networks are smart because they quit showing the anthem, so they're not advertising the protests, which are basically meaningless by this point anyway.