Lets take Islamic Terrorists as an example, they have a very wide pool of people to choose from, many of whom do not fit any stereotype you could come up with.
As soon as its known that security targets specific profiles, it becomes trivial to bypass security.
This is so staggeringly unlikely to happen. The TSA is more likely to find a winning Powerball ticket in someone's luggage.
If the "specific profile" is their ethnicity, then it doesn't become "trivial" at all.
It puts them through a huge new cost -- having to recruit and convince to send on missions more people of other nationalities. And while those do exist, they are far rarer than fundamentalist native Syrians or Iraqis for example.
Pick out the "true" syrians. Ethnicity is not a good predictor of appearance.