Sometimes it's not even direct consequences. You stand out as "that kid" and suddenly, you aren't given the benefit of the doubt the next time there is some kind of conflict at school. Or you are held to the rules -just a bit- more strictly than everyone else. Or, if your grade is on the border between a B+ and A-, they'll give you the B where they give the more obedient kids the A. When you become "that kid" the consequences can be almost invisible and insidious.

At least in the US, teachers and administrators are given rather broad latitude to treat students differently, without requiring justification and very often based on their own personal biases and prejudices.

The irony of (teacher) reciting a pledge in support of 'liberty and justice for all' and then falling apart because a child has tried to use some of that liberty, then wishing and perpetuating injustice upon them in retaliation, is strong.

If one's ideals fall over so easily, what would happen in the event of an actual serious attack on those ideals?

It's because it's not an ideal. North Korea does a very similar pledge thing where they call themselves the only democracy and so on. It isn't true, it's just brainwashing.