Yeah, IME they recite a script (I’ve heard it many times) where they explain why they are doing it, what it will involve, and how you can refuse (in that case, it would probably mean not flying that day). And offer to do it in private.
Mostly to make a point; more people are likely to care about it not being okay if it's phrased that way. (Something, something, toxic masculinity, "suck it up tough guy, can't handle a little pat-down?")
The fact that the TSA agent a woman doesn't automatically make someone else comfortable with whatever liberties the agent feels like taking. It's still likely worse if it's a man doing it, but sharing a gender isn't an excuse for the agent to do whatever they want.
That's not really an equivalent statement. In general, women do face more harassment and unwanted touching, which often doesn't translate to the "white" example you give.
I'm saying exactly the opposite. Your example statement being equivalent to the one I gave would imply that white people face more harassment, which isn't the case.