I just got home from Los Angeles.
Almost everyone was being scanned by a low-level X-ray machine at LAX. My wife and I refused and got a pat down instead.
I admit I am not a radiation expert, but, there is no reason to assume that these units are safe after repeated scans (radiation is cumulative) for frequent travelers, kids, women (breast exposure), etc.
In fact, I mentioned to the nice guy patting me down that I thought that the scatter from the units could be proven down the road to be particularly dangerous to TSA employees near the unit. He hazarded a comment that many employees were concerned -- did not trust the feds' claim that the units were safe -- but they needed the work!
As usual, the folks who OK this stuff themselves have little understanding of the science and are not subject to the same screening or at least frequency of screening.
My advice is to refuse as often as you can to be scanned. Ask to be patted down. Do not get angry at the poor TSA officer just doing his or her job. Do not get snotty with them. Just politely ask for what is your right -- a pat down.
In 20 years, if it is shown in retrospect that the scanners have been safe for as many years, you can get X-rayed.