It's not an invasion of privacy--but if the screeners detect nervousness in all, or mostly all, young Muslim males and then search them, the ACLU could go into search and seizure law which is another cup of tea, saying they are de facto profiling according to ethnicity.
I'm not a ACLU lawyer and I came up with that in a couple of seconds after I read your post.
Why would they detect nervousness in all or most Muslim males? Are they an unusually nervous bunch?