Why do they say "may not" for things which people shouldn't do

In this context, may means that you have permission to do something, so may not means you are not permitted to do something.

should is generally interpreted less strictly, as describing a desire or strong suggestion, rather than a requirement. So should not means that they would prefer or recommend you not do something, not that it's prohibited. For example, You should not go swimming during a thunderstorm.

Sometimes these can be conflated, though. You should not drive above the speed limit, because it's against the law and you might get a ticket.

In comments, John Lawler wrote:

May is a [modal auxiliary verb], and all modals have at least two kinds of meaning -- one kind, called Epistemic /ɛpəs'tɛmɪk/, refers to logical possibility and necessity, e.g. This may be the place means it's possible that this is the place. The other kind of modal meaning, called the Deontic sense, refers to obligation and permission, and is social, not logical. This is a case of deontic may, which refers to permission -- She may attend the ball, provided she keeps her shoes on all night.

More on modals and their epistemic and deontic meanings here.

I’ve placed John’s words here in a CW answer because answers help search optimizations in a way that comments do not.

I'm not sure "may not" has the same meaning as " must not"

Should not = suggestion

Must not = warning of a bad outcome

May not = authoritave denying of permission, or prediction of event