How come beltless front squat or ohp feels harder for the abdominal, when using a belt should make them contract harder?
Perhaps your sensation of “harder for the abdominal” is not quite accurate 
Probably. It’s harder to brace without a belt, and the abdominals seems to get more of a burning sensation. I assume it’s because the abdominal muscles is more of a limiting factor without a belt, but I’m not certain. Therefore I wanted to hear your take on it?
I don’t think the abdominals are a limiting factor for any barbell movement.
What might be the reason why it feels subjectively harder for the abdominals when doing beltless front squat?
Because you’re misattributing some sensation to your trunk muscles working “more”, even when they’re not.