So common that it has a name.
E.g. the lists literally include the 1936 (Nazi) Olympics, which is just about the textbook example of using a global sporting event for the sake of propaganda. Jesse Owens certainly threw a wrench in those (white supremacist) plans, however.
But I don't think "we need to care more" is a good mental model for the issue
For start, do not watch their events, and ignore them as far as possible.
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Reject hosting events organised by them. The same goes for olympics, fortunately most people are noticing that it is a waste of money.
(my city overwhelmingly rejected applying for winter olympics hosting after grassroot campaign by local people - I also participated in it a bit)
69.72% against, see https://en.wikipedia.org/wiki/2014_Krak%C3%B3w_referendum
Reducing public funding for professional sports would be also nice.
Now you say, oh, the members won't do anything. They are willing complicits. Guess what. They are also associtations and have members. In the end your local football club is a member of a local association, that is member of a national association, that is member of FIFA.
Why not start there. Start an initiative in your local club, that they take action on the next level, that they take action on the next level, etc. If you local club takes that up, but the next level ignores it, use your contacts to neighbouring clubs. If still nothing happens start an initiative that your club leaves the association.
If your local club prefers to do nothing, they are complicits as well. But you can leave. Get your friends to leave. You can still play football. Just meet up at a field. Place some posts. But stop complaining about the corrupt FIFA.
Fans can quit paying teams.
But teams don't care and fans don't care.
https://www.justice.gov/opa/pr/nine-fifa-officials-and-five-...
https://www.espn.com/soccer/fifa-world-cup/story/4501424/uef...
In any case, professional sports is intrinsically corrupt, and the billions in broadcasting rights money sloshing around the trough are a magnet for scum.
----
You're so nice
You're not good
You're not bad
You're just nice
I'm not good
I'm not nice
I'm just right
I'm the witch
You're the world
--Into the Woods, Last Midnight
Which isn't likely - all the people I know who were upset about Qatar hosting are sports fans in the first place and all got together to watch it regardless.
That's what gets me. Qatar can Qatar in Qatar, but the disgusting, corrupt, hypocritical ruling class who would preach to me and claim to be the "experts" on how I should live my life and to be my moral superiors is what gets me. And they're the ones who really enable and legitimize these regimes too. They're the real evil, and it's high time to put an end to them.
We need to strengthen our democratic institutions and of course also be more demanding of honesty from their leaders.
Just saying they’re evil and we need to put an end to them sounds like people saying the police is evil and should be abolished. A really bad idea in my opinion.