Mohammed is not their God. The picture ban is supposed to prevent Muslims from the temptation of worshipping Mohammed (a man) instead of God.

The rule is forbidding idolatry which is one of the defining differences between Catholicism and Protestantism.

I'm not sure what you mean here; do you mean Catholicism and Protestantism don't also forbid idolatry?

Protestantism shares a lot of its theology with Islam. It makes sense, because it is a reformation movement to restore Christianity to its Abrahamic roots. It includes things like abolishing the concepts of popes, priests, saints, or any holy individual.

It also includes forbidding idolatry. Images and sculptures and works of art should not be prayed to or venerated.

So the rule that you cannot depict Mohammed, God, or any other prophets is not to prevent disrespect. It's to prevent worship of images.