FIFA is mostly global, so setting one nation above another is weird.
True, but the point is that FIFA set the bar so much higher. The poppy isn't even political... it's rememberance, honours the war dead, and, as far as I'm aware, offends nobody. FIFA have recently relented and accepted it as an exemption, but probably only because of the lack of protest from other nations.

NFL are the regulators of US football and I would assume they issue licenses to players. They should realise that politics creeping into the sport is bad for business because it's divisive, and they have the power to ensure it doesn't happen, or at least if it does they can fine or suspend players, or even revoke their licenses.

It's bringing the sport into disrepute, and they're allowing it.