Also it can be (not saying that's the case here) used as a way to exclude undesirable politics while keeping desirable politics in place.
For example the "don't bring politics into sports" that was bandied about during the kneeling controversy in the NFL a few years ago. The National Anthem is political. All of the "support the troops" events during games (paid for by the taxpayers!) is political.
NFL may not be in as good of a position to distort the political environment as Facebook just due to the obvious differences between what they do, so maybe not seen as as much of a "threat" to the political order. But the NFL absolutely hides behind the same "no politics here!" curtain that Zuck is attempting to pull down. Nobody is really buying it from either company. Anyone who has watched an NFL game has seen the stuff you mentioned and more. It's absurd to say sports are not political .. of course they are! It's one of the few common grounds Americans have to stand together on, it is broadly politicized as a result.
Edit: grammar fixes