Now, there are various reasons why people don't want to have the full body scans, ranging from privacy matters all the way to safety. Physics can't address issues on privacy matters - it is a personal decision and what you are comfortable with. However, physics can certainly address the latter, which is the radiation safety issues. This is where I see many people are getting either the wrong information, or not realizing what they accept to be "safe" and what isn't.
What makes it a bit confusing is that, at least in the US, there are two types of full-body scans. There is one called the X-ray backscattering scan, and the other being the Millimeter-Wave scan. The former uses weak x-ray to do the scan. The TSA has cited studies in which the amount of radiation received during such a scan is equivalent to about 2 minutes of flight time at high altitude. There's some questions about this number, and some even quote it to be as long as 1/2 hour. Regardless of the number, it is still less than what you get with a dental x-ray, and certainly less than what you would get over a typical airplane flight. So one has to consider, just like having a medical x-ray, if this is an acceptable risk, or not. This is a personal judgment, but it should be decided upon a clear understanding of the radiation amount received IN COMPARISON with others that one has already accepted.
Now, the latter uses non-ionizing radiation, typically in the GHz range. So this is safe as far as "radiation" is concerned. Yet, there are those who are not aware of this. See this blogger, for example.
One report from a very credible source (a famous health author whom I know quite well) reveals that TSA officers told her the naked body scanners don't even emit X-rays. "It's a myth," the officer said. "There are no X-rays from those machines."
Really? Then how do they work? Are they MAGIC? Do TSA officers cast a magic Spell of X-Ray Vision on the air travel passengers like some sort of Dungeons & Dragons adventure?
No, it could easily mean that that scanner is the Millimeter-wave imaging scanner, and it is completely accurate that there are no x-rays from the machines. BTW, there is a very nice paper describing the physics of this technique that you should read if you're interested in this:
D.M. Sheen, et al., IEEE Trans. Microwave Theory and Tech. v.49, p.1581 (2001).
I think people need to make an informed decision here, rather than repeating the same irrational decision that's based on rumors and half-truths. If you know the difference between x-ray backscattering and millimeter wave scans, and you also know how much radiation you get when compared to other types of radiation, then go ahead and decide if you want to skip the scan and do a pat down. But don't decide based on confusing the two types of scans, or simply not knowing the level of radiation that you get when compared to other types that you've already accepted as part of your life.
And don't use the safety card to hide behind other issues. If you dislike the scan because you don't want an image of your pseudo-naked self being displayed on a screen somewhere, then argue it on that point, not on concerns about "safety".