Matt offers some good arguments why we shouldn't do it.
...the strategic costs of becoming a country that engages in systematic formal discrimination against Muslims are rather high. I would like to live in a country where if a teenage American Muslim reads on a message board somewhere that the United States is a racist country hell-bent on persecuting Islam that he thinks “no it isn’t” not “that’s why I got singled out for strip searches when we went on vacation last winter.” Nor do I want the Abu Dhabi Investment Authority to come under political pressure at home to divest from US firms because Emirati citizens who visit the US are being treated unfairly. Right now if a talented Bangladeshi scientist is weighing offers between an American and a European university, I can honestly tell him he’ll find the US a more welcoming place—that’s a strength we have as a society and as a country, and not something we should be eager to give up.But let me suggest that the throwaway line there "We could enhance security by making everyone fly naked, but common sense is that it wouldn’t be worth it." does suggest a solution.
The United States is a gigantic, diverse country that does business and policy all around the world. Air travel in this country is as safe as it’s ever been. Taking reasonable steps to make it safer would be nice, but cutting ourselves off from a huge swathe of the world and poisoning relations with 1.5 billion Muslims is going to be much worse than an exploding airplane. We could enhance security by making everyone fly naked, but common sense is that it wouldn’t be worth it.
We should have everyone who is going to get on a plane enter a room before boarding and remove all their clothes. Then they step into the next room where they are issued an airline-approved passenger's uniform with flight slippers for the flight. Their clothes and all carry-on baggage would then be packaged together and shipped (separately on non-passenger aircraft) to their destinations where they could pick it up upon arrival. That way everyone is discriminated against equally.
That might work, although it would give a whole new set of meanings to the announcement by the airline "I'm sorry, but we cannot find your luggage."