Why is the "have to" in "must have to" not redundant here?

It depends on what the speaker is trying to convey.

Using either "must" or "have to" asserts that the statement is truth.

You have to put in a password.

You must put in a password.

Those both convey the same idea that there is only one path forward and that the speaker is absolutely certain.

Using both "must" and "have to" in the same sentence creates a strong assumption.

You must have to put in a password.

This meaans "I'm not certain, but I'm very confidant that you have to put in a password".

Wikipedia explains it as:

When used with the perfect infinitive (i.e. with have and the past participle), must expresses only assumption [.]To express obligation or necessity in the past, had to or some other synonym must be used.