Libertarians claim that institutions and practices are only legitimate if they do not contradict objective property rights. It does not matter if an institution is an ancient tradition common to every society on earth (as, for example, chattel slavery was); if it violates objective property rights then it is illegitimate.
Similarly, it does not matter if a practice has widespread support or acceptance (as taxation has now and conscription has had in the past); libertarians still hold these practices to the standard of objective property rights and find that they clearly violate self-ownership.
The fact that libertarian condemnation of popular practices or institutions is controversial or unpopular is irrelevant. What matters is the veracity of libertarian principles.
With this in mind, it is interesting to review how libertarians have tackled the subject of circumcision. Some libertarians have made the obvious point that circumcision (despite being a widely-accepted practice) violates objective property rights, specifically the self-ownership of the child.
Parents must make numerous decisions on their child's behalf (and even sometimes against the child's will) as part of the parents' responsibility to remove the child from peril by raising him to the safety and self-sufficiency of adulthood. However, cutting off the child's foreskin is in no way justified by this responsibility. Most people accept that a parent has no right to tattoo their child, yet circumcision is a more egregious act of aggression than a tattoo.
The best article setting out the libertarian case against circumcision is this article by Walter Block and Patrick Testa. Other libertarians who have spoken out against circumcision include Wendy McElroy and Bryan Caplan. I have set out my own opposition to circumcision previously here and explained why I think any philosopher tackling issues relating to the family has a responsibility to speak out about circumcision here.
Very few other libertarians have written on the ethics of circumcision, but I did find this comment by Roderick Long in a discussion about what parents may reasonably do to their children:
when it comes to abusive procedures like female genital mutilation (popularly known by the euphemism “female circumcision,” falsely conveying the impression of being comparable in seriousness to male circumcision), we generally think parents do not have the right to do this, even though women who have had this procedure done when young will usually endorse it in retrospect when they are grown, because they have been inculcated with the relevant cultural attitudes and values. - Beyond Patriarchy A Libertarian Model of the Family by Roderick Long
There is a lot to unpack here. Long points out that the genital cutting of girls is an "abusive" practice. This is true: as a matter of principle, any genital cutting of a child by an adult is an act of aggression. No child can consent to such an act, girl or boy. So why doesn't Long also acknowledge that the genital cutting of boys is an abusive practice?
Long argues that the genital cutting of girls is so much more serious an issue that it is false to use the same word to describe it as the word used for the genital cutting of boys. Why is the core issue for Long the need to differentiate the cutting of girls as compared to boys? Whether or not cutting girls genitals is worse than cutting boys genitals is a bizarrely irrelevant distraction to the principle of the matter. All genital cutting is an act of aggression.
Long argues that genital cutting of girls should be called "mutilation". The definition of mutilation is the infliction of a disfiguring injury. This is indeed true for female genital cutting, but obviously it also applies directly to male genital cutting. Why then is it so important to apply this term to girls but not boys?
Lastly, Long makes the argument that if a child grows up to later endorse what was done to her by the parents, this cannot necessarily be taken as consent because the child may have been inculcated into this belief during her formative years. He makes this argument exclusively about girls. However, his argument obviously applies to male circumcision in exactly the same way. If he doesn't accept the later consent of grown girls to what was done to them, how can he accept the later consent of grown boys?
It seems like Roderick Long's aim in his comments on circumcision is both to denounce female circumcision and at the same time signal acceptance of male circumcision. There is nothing wrong with calling the genital cutting of girls "female genital mutilation" and denouncing it, although it takes no courage to do so since it is merely to voice an opinion already unanimously accepted in the West. But Long clearly doesn't apply the same standard to male circumcision. He does not want to call it "male genital mutilation" and he does not denounce it.
Libertarian philosophers should subject all social institutions and practices to the same question: does this violate objective property rights? If the answer is yes, then the libertarian philosopher ought to point this out. This is especially important in cases where such institutions or practices are widely accepted as legitimate, as male circumcision is. This is the most basic responsibility of a libertarian philosopher.