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You can say no to a TSA face scan. But even a senator had trouble.
(www.washingtonpost.com)
I've never personally had issues declining facial recognition at airports for normal domestic travel. For global entry they converted from fingerprint to facial recognition kiosks in the last couple years; not sure if you can avoid it with those. My one time entering the US with those, the attendants didn't know what was going on when I asked to not use facial recognition and just told me to proceed to the agent without using the kiosk, which was the wrong thing to do. Still got past the agent but got a talking to.