Libertarianism is based on simple principles. Your life. you decide. Based on that, self harm is no brainer. How supportive libertarianism on self harm depends on how radical their libertarianism is.
In general YES. Self harm is OKAY. When a person fully consent doing things that you or society think is self harming, that person should have full right to do so. Government should NOT interfere.
The most obvious black and white case "text book" of self harm is suicide.
You can read here
The answer is unanimously YES. Libertarians allow self harm, and in general, even suicide.
Jeffry Miron answer will be very similar to mine
The more difficult question is assisted suicide. Freedom to assist
someone else commit suicide might seem like a natural extension of the
freedom to commit suicide, but assisted suicide does raise the issue
of coercion. If assisted suicide is legal, it might be too easy for a
spouse or other family member to force someone into a "suicide" that
is really murder.
The issue is not whether something is self harm or not. The issue is whether something is consensual or not.
The ONLY exception is if consent is in doubt (other answers would quote, competent moral agent). Do we allow self harm when the actor is a child, not fully informed, yada yada yada.
Libertarians would prevent self harm. But libertarians would do so con sensually.
Self harm without consent is simply harming. And that's something libertarians and non libertarians are against.
In general it depends on whether consent of self harm is in doubt, whether the self harm act is "truly" self harm or just presumed to be self harm, or other things.
Consent matters a lot in libertarian. So whether an act is consensual or not would be a big deal for libertarians.
When consent of self harm is in doubt.
For example, say a person drink a poison that he doesn't know is poisonous. It looks consensual in theory, he drinks a poison con-sensually. But that's because he doesn't know it's poisonous.
A libertarian would say, you can force people not to drink it. Some libertarians agree that government have a reasonable reason to require proper labeling on most potentially dangerous food and drink.
You don't even have to be a libertarian to see that poisoning someone is murder and not suicide. And the state (for non radical libertarian), does have a case to prevent that.
Another sample is deceptive contracts. Libertarians in generals are against scams. But what count as scams or frauds is often grey. Look at Sim Lim scam. A person agrees to sign a contract to add insurance for his iPhone. http://www.asiaone.com/singapore/sim-lim-scams-student-reduced-tears-after-being-charged-1k-iphone-warranty
In theory the victim consent to pay by signing up the contract. In practice the guy that present the contract deliberately obfuscate the material term of the contract.
Again, as a libertarian, I have little issue if government would prohibit such things. That being said, as a libertarian, I really do not think government intervention will do much against such scam anyway.
Now let's take a look at something a bit "whiter"
However, once a person DOES know that the drink is poisonous, and he really wants to drink it, then he has all the right in the world to do so. That would be a standard libertarian ruling.
Perhaps a better question would be whether it's a good idea to use libertarian principles and allow self harm.
We all do things according to what we believe. Not allowing self harm means allowing other people, or government, to prohibits act, that they perceive as self harm to others.
What does that mean? That means government or anyone, can simply prevent you from doing anything you wish by declaring that what you do is self harm.
Usually typical prohibition against self harm is done by government prohibiting individuals from act that the governments or society deem self harm. Sometimes the individuals performing the act do not think they are self harming themselves.
In which cases, just like in most cases, libertarians would "err" on the side of giving individuals the choice.
How absolute libertarians are depend on how radical they are to libertarian principles.
Consider that the poison that you think is poison actually make someones' IQ higher and is not poison at all. Say other people have a right to stop people from self harming.
What would stop people from declaring that you are self harming when you are not really self harming?
What would stop me, from saying that you are harming your soul to hell if you don't pay me $1million and hence, I have the right to force you to give me $1 million.
You can argue that I am wrong. But that means I have to agree with your argument first before you can choose not to give me $1 million. Also, I have $1 million reason not to agree with you.
The more obvious cases are prostitution and drugs.
Most drugs are far less dangerous than cigarettes. Nobody dies due to ganja. Almost no body dies due to xtc. Even reasonably harmful drugs, like meth, can help autistic people when used properly and responsibly. Many people do that.
And yet, people, who are not customers, and have no incentive to be "right" on those drugs.
Most government in the world prohibit xtc, lsd, ganja, psychobilin, DMT, and so many things that do no harm at all. Half of jails are filled with people that do non violent crime.
Allowing the states, or the society, to prevent self harm, effectively give power for some people to simply "run others' life". That is very dangerous not only to the very people they supposedly "protect" but for society as a whole.
Not allowing people to self harm can be abused by the majority of voters and buy politicians to actually harm people they claim to protect.
I believe that the real reason behind anti prostitution acts is to put unnecessary burden on sexual transactions. Polygamy or temporary marriage can be very consensual. Criminalization of prostitution can be used to prohibit those 2 arrangements. However, prohibiting prostitutions is to the best interest of most males. Most males will have harder time getting laid if Donald Trump can easily pay 1000 women to fill his harem.
Hence, in most western countries, polygamy is prohibited. It's obvious.
As a moderate libertarian, I would require a very strong proof of self harming before voting in favor of candidate in government that wants to prohibit some self harm.