I was asked to talk about this awhile ago, so here we go. This is only going to be about male circumcision, as female circumcision is not practiced in Judaism.
Circumcision is a major symbol of Judaism, just like avoiding pork (despite the fact that shrimp and rabbits are also not kosher). Indeed, in ancient times when Jews came into contact with Greeks and Romans, it was used as a sign to determine who was Jewish. Circumcision became more popular in the West in the 1900s, especially in the United States, and notably, Korea. Additionally, it is very common in religious countries, such as most of the Muslim world, Israel, Central Africa, and the Philippines. Australia also appears to have had a flirtation with the practice in the mid to late 20th century, but it is declining heavily. There is a divergence in when the procedure is performed. In the United States, Israel, and possibly Korea, it is performed at or near birth. In most other religious contexts, it is performed around puberty, where it can be more controversial and painful (explicit video).
The practice is mandated by Torah, meaning that it is required of all male children and converts:
Genesis 17:10-14 This is my covenant which you are to keep, between me and you and your seed after you: every male among you shall be circumcised. You shall circumcise the flesh of your foreskin, so that it may serve as a sign of the covenant between me and you. At eight days old, every male among you shall be circumcised, throughout your generations, whether house-born or bought with money from any foreigner, who is not your seed. Circumcised, yes, circumcised shall be your house-born and your money-bought (slaves), so that my covenant may be in your flesh as a covenant for the ages. But a foreskinned male, who does not have the foreskin of his flesh circumcised, that person shall be cut off from his kinspeople- he has violated my covenant!
Leviticus 12:3 and on the eighth day, the flesh of his foreskin is to be circumcised.
Then, there is the concern of the Paschal Lamb:
Exodus 12:43-44,48 YHVH said to Moshe and Aharon: This is the law of the Passover-meal: Any foreign son is not to eat of it. But any man’s serf who is acquired by money-if you have circumcised him, then he may eat of it. … Now when a sojourner sojourns with you, and would make the Passover-meal to YHVH, every male with him must be circumcised, then he may come-near to make it, and will be (regarded) as a native of the land. But any foreskinned-man is not to eat of it.
Elsewhere in the Tanakh, being uncircumcised is used as an epithet ערל (`areil), usually against the Philistines.
It is clear that circumcision is required in Judaism, but does this mean it is acceptable in libertarianism? If a religion said to go around and behead other people who have done nothing wrong, that would clearly be unacceptable to libertarians, who oppose aggression. It is not entirely clear where circumcision falls in on this. It is a procedure done without the consent of the acted upon, but that does not rule it out as unacceptable. If an infant was choking and needed a tracheotomy, it would be unacceptable to not order the procedure done. Indeed, it seems valid for the parents or caregivers to order a medical procedure on behalf of someone who cannot consent theirself.
There is an objection that circumcision is not a necessary medical procedure. From what I have seen, research literature seems to be a wash as to whether it provides any health benefits. Some studies say it does help, others say it does not, or may hinder health. And then there are the issues of whether it harms physical sexual sensations. Studies on that also seem to be a wash. The only way to really be sure of that is to study men who have not been circumcised at birth, but later are, and have experience both ways. Of course, there may be a bias that those who want it will be more likely to validate their decision. I know of one Jewish man whose mother did not want him circumcised, had the procedure done on his older self, and is satisfied with it. Again, he may simply be affirming his decision, a psychological coping mechanism. There are simply too many variables in the health and sensation aspects to really judge this at the moment, which starts to sway the debate against the procedure.
However, we are blessed with a convenient analogy. Many parents see fit to have their daughters ears pierced. They think it looks cute and helps clarify the sex of the child. Personally, I think it looks ridiculous. It clearly involves piercing the skin of the child, and likely causes some distress and pain, but is it really such a horrible thing to do? Is a girl harmed for life by this? Certainly, it is less invasive than a circumcision, but the fundamental is the same. If this is acceptable, circumcision likely is. And I think its a bit over the top to say its an aggressive act to pierce the ears of an infant.
It would be much easier to resolve this if the practice was commanded at puberty or adulthood, as most cultures that have it do. Then, the individual could decide for themselves, and many would. Unfortunately, for some reason, Hashem has insisted that it be done on the eighth day of life. Perhaps there is a very good reason to do this as opposed to much later.
In my view, circumcision is not an aggressive act. If one feels the medical aspect supports the procedure, then there is no complaint. If not, then we have to consider the overall morals and compare this to other situations. It seems to be making a mountain out of a molehill, and there is an argument (I am unable to find whatever blog mentioned this) that a child could sue his parents for doing it. If they raise him religiously, nine times in ten, he will be satisfied it was done. I am, and I was raised conservaform, grew up atheist, before becoming religious. That one in ten may be the price to pay, and even among them, he may be dissuaded from it in order to preserve a good relationship with his parents. Ultimately, this feels a less important question of those that vex us, and I certainly believe that libertarianism has an onerous purity test that no one can ever truly pass.