Rafi says God commanded us to “violate it [the NAP] in the case of circumcision” . On EPJ  you add: “I believe God has commanded me to follow the NAP in (almost) every other case I can think of”. I agree. But this cannot be compared to “Minarchy” – which you started off with .
The only acceptable Torah model is a zero state! There is a senate (Sanhedrin) and constitution (Torah), whose members must be accepted by the public, but these are purely religious, and so have delineated duties of ensuring the public welfare (physical and spiritual). This is equivalent to membership in a community with its own rules. I disagree with the nascent Sanhedrin’s political model . There is no parliament nor mob rule, no congress nor dictatorship. “Theocracy” (as put by Josephus) is a neat description, but not in the Iranian sense of a clericalist dictatorship. See more on the democratic nature of criminal justice in Chazon Ish Yoreh Deah 2:16 (end). Law enforcement, to exist, must be regarded by all as excessively lenient.
By the way, while we suffer from a state in the meantime, we ought to fight to separate religion and state , for many reasons, but mainly so as to free religion from outside control (Yeshayahu Leibowitz).
The king (or quasi-king, like Moshe and the Shoftim), too, is but a religious figure (as proven by Hak’hel, etc.). His sole purpose is to ensure the Jewish people do not sin. Of course, a king is a necessary evil, anyway, including Moshiach, and his monarchy is a limited one. God forbid any secular statehood be considered legitimate, even after the coming of the Messiah, contra Satmar. Yes to Jewish sovereignty, as an autonomous society (Yad Yisrael tekifah); no to any form of coercive state.
Note, I am not saying one form of government is more prosperous or peaceful than another. We accept the yoke of the Torah with its obligations and prohibitions, and coercive taxation is always theft.
Rafi says  he will deviate “Up to here, and no further”. But Judaism and libertarianism diverge in other areas, as well. Both Judaism and libertarianism are prescriptive. How can they not be contradictory at times?
Indeed, there is a huge chasm between Natural-Rights (or Hoppean) libertarians and Jewish Libertarians. Our point of departure is that Judaism assumes freedom and non-aggression only as the approximate default position, to be continually re-examined on a case-by-case basis. The freedom philosophy must be subsumed under the “Derech Eretz” categorization of Torah law to have any validity whatsoever. Our Rabbis have many legalistic explanations as to why one may not trespass, steal or damage property. The non-aggression axiom or negative rights is the axiology behind much of monetary and war jurisprudence, but with many exceptions and divergent applications.
Property rights in one’s own person conflict with prohibitions against harming oneself (“את דמכם לנפשותיכם”), because the body is considered to be partly owned by God. God owns us, therefore we may not own Jewish slaves for too long, we may not commit suicide, “Evictionism” is even more wrong for Jews, and more.
Even our national ownership over the land of Israel is not without caveat, see here . In truth, we are not “plumb-line libertarians” at all, but Jews who believe we have uncovered more of the true meaning of Judaism with the help of libertarian insights (as “Chochma” permissible for us to accept, but not as “Torah”).
[Why the “chauvinism” regarding the non-Jew? One may not remain a non-Jew. (Rafi’s note: I do not understand this point. One may of course remain a non Jew.) The courts try to discourage conversion, yes, but only because one must convert for the sake of Heaven. I stand with Yeshayahu Leibowitz in rejecting the supremacy of any manmade morality over the Omni-supremacy of Torah law (which has what to say about everything!).]
I am somewhat unsure about the conclusions of Walter Block’s essay, even for non-Jews, as I will explain below. But no matter. Arguendo, Bris Milah is the perfect proof that Block is wrong when he claims , with Rothbard, that it doesn’t matter at all how one came upon libertarianism, only that one did. He further wrongly asserts  that any religion is fully compatible with libertarianism. As Rafi justly pointed out, what about Milah?
Here  is another illustrative example, straight from Block: “Suppose that Martians beam down a message to us earthlings: “Kill innocent person Joe, or we blow up the entire earth.” (Stipulate that they have the power to do this, and we are unable to stop them.) One would hope that a hero would arise to murder Joe, so as to save the planet. We would then hold a ticker tape parade in his honor. Afterwards, the heirs of Joe would have the right to exact full punishment against our hero.”
In the Torah view, one may not kill Joe at all. Instead they should all give up their lives. Joe’s murderer would be treated the same as any other murder (and parades are “Innui Hadin”, of course…). I assume Joe is Jewish (Yerushalmi Shabbos p. 77a).
Let us continue. Judaism disallows the free market choosing its own medium of exchange (seashells, rocks, prison cigarettes, etc.), obligating a national gold standard so as to observe the obligations of Ma’aser Sheni, etc., see Chazon Ish Yoreh Deah 72. (Rafi’s note: I’m not so sure about that from my own study of Perek HaZahav, but do not know enough yet to rebut. Just because the Chazon Ish said something doesn’t mean it’s הלכה למעשה)
Many believe  that “The Biblical maxim to ‘love your neighbor’ and the libertarian principle of non-aggression are essentially synonymous.” To Xtianity, perhaps this is so, but the true Torah admits no such thing. The verse refers to Jews alone, and this stems from love of God leading to love for fellow co-religionists.
Finally, Austrian economics seems to be simply more accurate scientifically. Our scriptures and history are laissez faire capitalistic, too. Judaism is concerned with the real world, so, obviously, we are partial to real science as opposed to Keynesianism.
An additional value of libertarianism is in its being a great beginning foundation for the laws non-Jews are commanded to write for themselves (in the seventh Noahide commandment).
[For the record, current mainstream Judaism is lost in stygian interventionism, antinomianism, etc. I speak here of Judaism as it used to and ought yet to be, not as it is currently construed.]
As pledged, I will now comment on circumcision, as regards libertarian legal theory. This will become relevant when libertarians “rule” the world.
First to Rafi :
Yes, the act is necessarily violent. So what? If it can be established that it is a “clear benefit to the child”, the NAP is cancelled out by the guardianship rights of the parent (as Block explains). As I wrote in my previous comment regarding the NAP, “it is a theory of punishment”. Again, there is no just cause for compelling  war against religious Jews, only meting out punishment, if the child (who is the sole victim) actually demands it when he matures, no more.
Incidentally, Jews aren’t the worst offenders of the NAP. Blockian Libertarian Nuremburg Trials will be plenty busy with other “criminals”… Clean your own backyard first!
Now to Block :
Before I start, let me echo Rafi, Shimshon Weisman (in comments on the EPJ) et al. in affirming loyal Jews will forever flout the NAP in this regard (as explained above).
As for the legal question, firstly, I restate what I said before . Aside from societal conformity being a sufficient justification for surgery for Polydactyly and the like, which are done routinely, the legitimate Jewish ערל (as in his two younger brothers died after Milah and he is left uncircumcised legally) is forbidden from eating the Korban Pesach, prevented from prophesy, etc. Also, yes, he may indeed regret the circumcision later (as apostasy, likely, but not simply for lessened sensual pleasure!), but the pain endured should he later wish to circumcise (highly likely) is severely more than that of an infant. Circumcision reversal without surgery, which Block pays no attention to, is usually painless . The acceptable boundary of aggression probably suffers from ye olde “Continuum Problem” (a neonatal lack of intellect lessens the pain, “Veyosif da’as yosif mach’ov”).
Second, the data assembled suffers from selection bias. The core medical evidence presented does not overwhelm; some of it is tentative or based on procedurally faulty statistics, which are also quite dated (medicine has gotten a lot better since 1950, and this will continue). Expert Mohalim (solely for Jews) vastly reduce the dangers he mentions, too, which the numbers overlook.
11. Ron Paul thinks so, too: