But another, more rational, part of me says that this is a total non-issue for the simple reason that there's nothing new about it.
Here's why: You've been required to show your photo ID (drivers license or passport) at the airport for years. And every drivers license or passport has your birthdate prominently emblazoned on it. So this new policy is simply asking for information that the airlines and the TSA already had access to.
I suppose there is some additional risk to civil liberties from the government actually collecting the information. But probably not enough to make it worth making a scene by "refusing" to give my birth date.
(I tried this once when a clerk at Motel 6 demanded my birthdate in order to rent a room, but when she cited corporate policy and refused to budge, I caved rather than going in search of a new motel. Yup, I'm a pushover.)