Is it a crime to want to live under the caliphate instituted by ISIS?

In the US that would (rightly IMO) be protected speech. More concrete “material support” would be required for it to be a crime. Though, I believe, distributing material actually produced by a terrorist organisation would sail pretty close to the wind (though IANAL)

That just proves that you are not really ‘at war’ with the terrorists.
In the real wars supporters, or even those with a chance to sympathise with the enemy, were certainly targetted.

IANAL either … but I think it depends on what the distributed material says … if it’s directly soliciting cash donations to ISIS, then I believe we’d be over the line … however if the material was advocating removing ISIS from the list of terrorist organizations, then I think we’d be okay …

Nope it shows that a small number of well defined rights (like the US constitution) is a better than an bloated amorphous collection of them (like the EU human rights charter)

Not that the Constitution is a perfect protection from the government doing awful things to its citizens, especially during war time. But it does a much better job than its more complicated alternatives in other countries.

Clarion, an anti-extremist organization, puts *Dabiq *and *Rumiyah *on its website (ISIS recruitment magazines.)

That doesn’t mean it is legal to do so. I just means it is not in the interests of any DAs to prosecute them for doing it.

Based on a Googling, it looks like it could be illegal, but no one has actually been prosecuted for it, yet. The closest is the case of Tarek Mehanna in 2012 (bolding mine):

http://www.thedailybeast.com/articles/2015/02/23/justice-department-we-ll-go-after-isis-twitter-army.html?via=desktop&source=twitter