I think that you are confusing two slightly different expressions.

'I can't stand this' means 'I can't bear this'.  If eating spinach makes you feel sick, you might say 'I can't stand spinach'. If you hate rap music, you can say 'I can't stand rap music'.

'I won't stand for this ' means 'I refuse to tolerate this'. If a pupil is rude in the classroom, the teacher might say 'I won't stand for rudeness in my class'. This means that this behaviour is unacceptable.

As you can see, the meaning is different.

Agreed. It has nothing to do with a British vs. American usage.