it's a protest for civil rights.
And your mass-market product being politicized is bad for business. Especially with political polarization being as crazy as it currently is in the United States.
When the target of your product is EVERYONE, you dont want to take a side in a political fight and alienate 50% of your viewership.
I think the NFL's decision reflects a will to try to not take a side in this fight, but rather to inforce a non-politization of their product.
Here's an exemple:
In the news media business. There are niche news product serving a political side in particular. Like MSNBC serving news to Democrats. Or Fox News to Republicans. Or the Daily Wire to Conservatives. Or The Young Turks to Progressives.... etc....
These target a political base. And the rest of the population is left out.
But there are also mass market news organizations. Like the Associated Press. The Associated Press lives by being 100% unbiaised, accurate, fair, NONPARTISAN. Because if they became politically partisan, they'd lose half their business.
The NFL is like that. They desperately want to be "The Assossiated Press" in people's minds. They do not want a (D) or an (R) in people's minds next to their name. Because that's bad for business for a mass market organization.