we don't have a history of supporting military dictators, nor do we have any kind of suppressed desire to do so.
Yes you do, just not in the context of a domestic government.
They can't investigate a legitimate religion
Define legitimate religion...
A religion is a large, popular cult. A cult is a small, unpopular religion.
Of course it's unrealistic armchair-libertarian drivel: the magnetosphere is a harsh mistress, after all.
What's interesting about this development is that it isn't a nearly-entirely American endeavour, which is often the case with such ambitions; Asgardia seems to be Russian and the AIRC supporting it is Viennese. I suspect we'll see a lot more anti-authoritarian behaviour from Europeans in the coming years as a) the EU weakens, b) the Internet transmits political memes that were previously comparatively contained by media limitations like talk radio and poor English literacy, and c) people already exposed to (b) come of age.
The much more feasible version of "let's get off the Earth so we can get away from our countries' laws" is called seasteading, and generally involves a platform in international waters. There's one clear non-Libertarian, non-American example of seasteading (Sealand, UK) which is fairly old and unusually successful by micronation standards. These days, however, the idea is generally associated with these guys, who have been funded by Peter Thiel. They, unquestionably, are primarily concerned with ways to dodge regulation. Without a realistic means of building such a gigantic physical presence, though, they certainly aren't going to be doing much of that; at best they'd end up creating their own passports that no one would accept.
"This isn't brain surgery; it's just television." - David Letterman