I usually try to play it cool until the moment the point me toward the radiation machine. Then I say "I'd like to opt-out". They are always very professional about it, and have a procedure (different in different airports) where you basically stand there and watch other poor suckers go through the machine, until they find someone to pat you down.
The reason I play it cool is because about 1/3 of the time they end up pointing me toward the regular metal detector at the last minute (I guess I'm not a cute girl...)
I always opt-out, and it's never been a civil affair.
The _least_ obnoxious was when the TSA agent heard my "I'd like to opt out" message, shouted "REFUSAL", made me stand _next_ to the scanner for approximately 15 minutes before finding someone who could pat me down, occasionally glaring at me for effect.
The pat-down was respectful, though it was done inches away from my 9 year old daughter, but the core of the issue, to me anyway, is that I object to both the new scanners AND the pat-down.
I've adopted an "only fly when I have to" policy, which meant 6 hour drives replaced flights to New York, but there is regrettably no way of avoiding all my business travel in lieu of driving.
I was raised by lawyers, and I think from that I learned how to present myself in a way that is both courteous and has a subtext of "the paperwork involved in fucking with me will crush you." The easy to articulate bits of this include good posture, eye-contact and precise diction. There's probably more to it than that which I'm unaware of. This also seems to work when I get pulled over.
Wish I could help more -- I think if you appear deferrential to the law (more so than the officer), it helps remind the law enforcement officer that they are also subject to the law.
I fly frequently and always opt-out. My standard response is to wait until I am pointed towards the AIT scanner, then say "Respectfully I choose to opt out." Jchrisa is right, there is no reason not to be courteous, and there is a better way to handle yourself than to be grumpy or annoying.
Sometimes they do yell out "Opt Out" loudly, but I don't mind because it alerts someone to come pat me down, and when the security is short-staffed sometimes the wait can be a bit.
For the record, I've never been discourteous. While I might loath their professions, I do understand that they're just doing their jobs, and I respect and appreciate that.
Also, to jchrisa's point, I can't imagine what, if anything, I might be doing to foster negativity. I'm a professional white male. I sometimes travel in suits, which may set off some innate animosity, but I've experienced the same negativity dressed in plain clothes.
I've often been described as "friendly-looking" and "approachable", and am careful to ensure that my demeanor isn't in any way offputting while I'm at the airport.
I'm not saying that I'm the nicest guy in the world or anything, but it genuinely surprised me to hear that other people who opt out don't share my experience.
The reason I play it cool is because about 1/3 of the time they end up pointing me toward the regular metal detector at the last minute (I guess I'm not a cute girl...)