There are too kinds of profiling: racial profiling and behavior profiling. There's a stigma that TLV security does a lot of racial profiling. The majority of security, however, is done via behavior profiling. There's no reason the TSA should refuse this kind. This violates no amendments or "ideals." It doesn't care about your dress, skin color, or religion. It cares about how you're acting, how you respond to questions, etc.

In TLV, there's an initial security check upon driving into the airport complex, which is quick with just a couple of questions, followed by a preliminary questioning while waiting on line to check-in, followed by the regular hand check. During all this time, there are plainclothes security officers walking around the airport and monitoring the whole airport from security cameras, one-way mirrors, etc. They aren't looking at your race - they're looking at your behavior. And they're quite successful.
Do they do racial profiling as well? Yes. But not on a level even close to the stereotype surrounding. Has it succeeded? Yes

Even if the TSA doesn't want to do racial profiling, they can at least do more behavior profiling and ween themselves off of "guilty until shown maybe not guilty." And this would not treat everyone the same.

A big problem with TSA security is the initial check is done at the hand-bag check. In Israel, checks have been done before you get to the airport, combined with intelligence to know if something is going on, as well as perimeter security on multiple fronts...