Changed my mind
On the subject of "we do this all day so it isn't a big deal" (which was the basic argument of the security guys) I was thinking that's fair enough. After all, other professions are in similar positions. I've done theatre work and, frankly, back stage, there are a lot of very attractive people wandering around in little or no clothing. You become blind to it after a while (no sniggering!). Doctors see patients in various states of undress and all kinds of weird and wonderful things besides. For some professions it is just part of what they do and, having been in that position, it isn't a big deal.
Then I remembered a recent story about a woman suing her gynaecologist for sexual assault. It only takes one perverted little shit and I'd really rather not take the risk that someone like this piece of scum (http://www.google.com/url?sa=t&source=web&ct=res&cd=5&ved=0CBAQFjAE&url=http%3A%2F%2Fwww.three.fm%2Fnewscentre%2Fisle-of-man-news%2Fteacher-charged-with-sexual-offences-552&ei=J9JZS5TLGMyTjAfmyJ2aAg&usg=AFQjCNEo71VC8t5u8RqHpOwlKFP6iUkc6Q) - who worked at the school my kids will soon be going to - got a job in airport security because he didn't need to be checked.