Waving a Mexican flag seems like cheering for a different team than your home city. It shouldn't feel like that, it should be fine, but it seems just a little strange if you are not Mexican, and a little disloyal somehow if you are.
Waving a Ukrainian flag at Putin seems like cheering for your team against one of your rivals.
Something like that. I can't articulate it how I want to. But it makes sense to me.