See here for a bunch of things to read (http://en.wikipedia.org/wiki/Backscatter_X-ray#Health_effect...). According to this page, 42 minutes of ordinary living is sufficient to give you a similar dose of ionizing radiation compared to the backscatter machines. It's certainly possible that the FDA is lying to us, but it seems more likely that these machines are indeed harmless. Sounds to me like the people saying "I avoid things until I'm sure they don't cause cancer" are throwing science to the wind and embracing a line of thought they wouldn't if they didn't already have some other reason for opposition.
I suppose it's possible for someone to be genuinely concerned over these very small quantities of radiation. But it strikes me that for the average person what underlies the panic is
1. a counter-factual belief that more health-harm is done by a new technology than actually is,
2. a diversionary appeal to concern for safety when health risks are not really a significant negative of a new technology.
This happens in all kinds of areas. Artificial sweeteners, GMO foods, irradiated meat products, and vaccines have all fought or are fighting this battle. The only reason this type of thinking is given a pass here or anywhere reasonable people congregate is because the community is so opposed to the technology for other reasons.
This might sound like a good thing, but it also means that the radiation isn't "diluted" over the full mass of your body. The damaging effects will be localized to -- and concentrated within -- the skin and shallower tissues. So those organs affected are getting a dose that's disproportionately much higher than the guidelines for full-body dosage considers.
Think of each cell in your body as a dice. When a cell is hit by radiation, the dice is rolled - you get cancer if any dice comes up 6 (these are billion-sided dice). The radiation dose is the number of dice rolls you need to make.
Now, under which circumstance is a roll of 6 more likely? If you roll 100 dice 1 time each (traditional x-ray), or 1 dice 100 times (backscattered xray)?
Edit: Maybe this is incorrect when it comes to cancer risk, but I had the impression it still mattered, with multiple impacts in the same area of DNA causing things to be more likely to permanently break. Unless that is extremely unlikely to happen at all at this level of dose.
Still, these machines are probably not particularly harmful.
Backscattered X-rays are not remotely near that point.
edit: Just want to respond to this: I had the impression it still mattered, with multiple impacts in the same area of DNA causing things to be more likely to permanently break.
This is called the multiphoton effect. It's real, but it's more important for radiation by low frequency radiation (e.g., cell phone microwaves). You can observe this in gases with high powered lasers or microwave resonating cavities. Weird things happen in this regime, such as stabilization (more radiation -> less ionization).
I suppose you could have molecular effects from multiple photons (e.g., one photon damages the DNA, a second damages the repair mechanism), but this is vanishingly unlikely at the doses we are discussing.
The same radiation distributed through the body will cause fewer errors per strand and be corrected.
To be fair, I haven't found any studies either way on the safety or danger of the 10 C.F.R. 20 limits, probably because very few people get close to hitting the dose limits. One study I found[2] that surveyed radiation workers in three different studies concluded that the relative risk for a sustained protracted dose of 10 Rems compared to no dose is 0.99 for cancer excluding leukemia, and 1.22 for leukemias. This means, as a radiation worker, you're somewhat less likely to get a non-leukemia cancer, and about 20% more likely to get leukemia. This is for a dose that is over a million times larger than what a backscatter machine will give you. Furthermore, these risk rates are lower than what would be expected from a linear estimate based on cancer rates in atomic bomb survivors, suggesting that smaller radiation doses are safer than larger ones, and the dose these machines give you is about 200-500 times smaller than the does you're going to get on the airplane (if you're flying cross-country).
I just wanted to put in perspective that the dosage these machines put out is extremely small when compared to the dosages you might normally receive, let alone the dosage which radiation workers commonly receive. Their health effects are minimal, and if they actually contributed to the safety of passengers, I'd say they'd absolutely be worth it. The real travesty here is that they violate privacy for no real gain, not that they are in any way a significant health risk.
[1]: http://www.nrc.gov/reading-rm/doc-collections/cfr/part020/
[2]: http://www.jstor.org/pss/3579020 (JSTOR link. If you're not affiliated with an academic institution, you'll only be able to read the first page)