My question now is are there any moral, ethical or legal obligation to bar a person from gambling after physically observing that he is mentally unstable?
if they are not causing any disturbances to the betting station or anyone, there's no reason to bar them, it's their money they have the right to bet, if nothing in the betting station that says specific people are forbidden from entering, then they should be allowed, and they have to give good reasons why they are barring these people, if they do not allow them.
Gamblers have different characteristics as long as they do not cause harm or inflict damage, we should not look down on them and let them bet.