A simple paradox. The “bad guys” are being profiled, AND it just so happens in this case they are “bad” in the name of their religion. People get religious accommodations in the US everyday. Any ban for any reason on anyone (that just happens to be Muslim) will be called a Muslim ban by someone for some reason.
Why re-write the EO. If narrowed, the next step the Judiciary would take would be to narrow their focus and examine the nature and “fairness” of the vetting of non-citizens that are being vetted because of their religion. The end-game is to extend US Constitutional rights to non-citizens world wide.
In this matter, the Judges have already found that a US citizen could have an “interest” in a non-citizen.