Maybe I'm missing something incredibly obvious, but one way to make much less invasive is to hire both male and female specialists and only allow a person to be scanned by someone of the same gender.
It sounds like the reasoning behind this sort of attitude (also seen in the frequent requirement of using someone of the same gender to frisk people) is that someone of the opposite gender must be heterosexual and would "get off" on seeing/frisking someone of the opposite sex.
But the screener could easily be homosexual. Or bisexual. But I really doubt if they're even asked what their sexual orientation is. And, honestly, do you even care if they get off on seeing/frisking you? How does their stimulation or lack thereof hurt you?
Another explanation for this sort of attitude might be that people are simply embarrassed when seen/frisked by someone of the opposite gender. But the reverse could just as easily be the case. Someone might feel no embarrassment from being seen/frisked by someone of the opposite gender, but might feel embarrassed by someone of the same gender.
Mandating that everyone be frisked by someone of the same gender based on these flimsy justifications makes no sense to me. If these are concerns at all (and they clearly are for some people), it's much more reasonable to simply allow the passenger a choice of being screened by a male or female screener.