"The constitution gives POTUS the authority to do what he did. Period."
Please cite the exact text of the Constitution where this is stated, then. Please note, also, that the Bill of Rights (where discrimination against religion is forbidden) was ratified AFTER the original Article II, therefore anything it says takes precedence as official Amendments.
And don't give us that bit about national security because if that were true, Saudi Arabia would be on that list (since the 9/11 hijackers and the Al Queda mastermind all came from there). Also the US would be banning ITSELF since homegrown terrorists have committed atrocities as well (Oklahoma City in particular).