You mean like the French Muslims, that are French citizens?
Ban French Muslims and you'll have major problems with France -- who, Muslim or not, a French passport not being honored would be a severe diplomatic insult. We would be inviting retaliation against American passport holders.
Practically speaing, allied nations are obligated to trust each others' vetting of their own citizens.
The fact is, as President, Trump would take a different stance -- more akin to Cruz' proposal.