It has been suggested that this is somehow a violation of academic freedom because something a guy wrote for his PhD got him fired.
If the message here is that you can't examine controversial ideas in academia, then we all lose.
— Gartenstein-Ross (@DaveedGR) May 10, 2013
There are many issues here, but I just want to focus on one--what is meant by academic freedom? Well, first, the guy was able to get his controversial dissertation approved, so that is one bit of evidence that one can examine controversial ideas in academia. More importantly, academic freedom exists in the academy. If you leave the academy, do not expect that freedom to come with you. That is one reason why we professors tolerate low wages--the job security that comes with the low wages and heaps of uncertainty upfront is compensated by the academic freedom that comes with tenure. And there are plenty of folks using that freedom to say all kinds of controversial things, like the Boston bombings were a false flag operation.
But if you leave the academy, you leave that freedom behind but you take with you your record of research. So, it is not like Vegas, where what happens in Vegas stays in Vegas. Nope, what you say and do in the academy can follow you around. So, if you join a research center/think tank that cares about its image, it may dump you if your ideas from the past (and, let's be honest, this guy has not dumped his old ideas) come back to haunt them. I am not a fan of Heritage, but they are a think tank, they have an corporate identity. So, it is well within their right to hire and fire people based on whether their ideas fit with their corporate culture/strategy/whatever.
That it happened so quickly might suggest that there was a rush to judgment. The bigger point here is that if employers are going to look at people's facebook pages and twitter accounts to see if they are suitable hires, you would think that a think tank would take a look at least at the abstract of a dissertation before hiring someone to do .... research!
Anyhow, there is no violation of academic freedom here. You leave the academy, you lose the magic protections that come with the old buildings and the ivy on the walls and so forth.