Hate to say it but FIFA's right.
The poppy has become hugely politicised, particularly since the wars in Iraq and Afghanistan. A national campaign to commemorate war dead is innately political we're not talking about a private commemoration like a funeral here. There is huge pressure on public figures to wear them, including shaming and threats towards those who don't, because it's politicised. Jon Snow has to explain why he doesn't wear one on TV every single year; Charlene White, who doesn't wear one on TV for the same reason, has the same thing with the added bonus of racist and sexist abuse. And the insistence that it isn't political in the face of all this is an attempt to shut down the criticism of the browbeating.
Let's not forget that no football teams, clubs or internationals, wore poppies on their shirts until 2010. England didn't do it until 2011. England and Scotland played each other two days after Remembrance Sunday in 1999 (Euro 2000 qualifiers) and neither team wore poppies, laid a wreath or even held a minute's silence. That wasn't controversial then why is it now? Politics.
FIFA isn't arbitrarily coming down on a long-standing tradition but rather enforcing its existing rules and not letting us be special snowflakes on this issue.