No problem, we'll profile dirt bags with ponytails too.
(Sorry, but I still live in an Ozzie and Harriet Leave it to Beaver world, where a dad exchanges his suit jacket for a cardogan sweater on arriving home from the office, leaving his white shirt and tie on while sitting down to the dinner that mom made. And only the women have long hair--always.)
Simply traveling under false names and passports would get them through. People need to stop kidding themselves that Arabs (or Muslims) for that matter have a big "A" or "M" branded on their forehead. There's no simplistic narrow profiling answer.