That's what I thought, too. Using "The NSA" in the way the shirt does is making a political statement, which is protected by the USA's First Amendment. It's one of the few rights that the USA Supreme Court has defended zealously.

Supposing that "The NSA" is some kind of "intellectual property", using the phrase as that tee shirt does is almost certainly fair use. This is a lot less certain, as you'd have to go to court, spend lots of money, and admit to infringing to plead fair use, so it's probably not worth the effort.

Zazzle took down almost every parody shirt I've ever made - even ones with custom artwork.

For example I made a "Yo Bama Bama" shirt that had custom art of Obama wearing a Yo Gabba Gabba hat with various phrases... that was taken down.

Custom artwork of video game characters saying stupid things... always taken down. Anything that referenced some sci-fi movie or TV show was always taken down. I'm surprised the NSA even had to complain. Zazzle preemptively stifles free speech when it's obvious it's a parody before anyone complains. Zazzle is so bad about this - I don't use them for anything anymore.

Well, technically you have no right to or expectation of free speech on Zazzle. I'm sure it's in Zazzle's terms of service that they can reject any product submitted to the site for any reason. I don't like, but it's their site, they can do that if they want.

They're probably just being overly risk averse to try and avoid lawsuits.