Anarcho-capitalism is a half-oxymoron/hypocrisy from my point of view. Anarcho-communism is a straight up oxymoron because ancoms are against political slavery (state) but are simultaneously for political slavery (communism).
Ancaps, on the other hand are against political slavery, but have nothing against economical slavery (corporatism, which is an inevitable consequence to capitalism just like communism is an inevitable consequence to socialism).

If you say otherwise, imagine this scenario: You see society as largely degenerate, and wish to have nothing to do with it. For that reason, you go to a forest or some place in Nature, build a hut/small house and live off of hunting, fishing and permaculture, with no dependancy on the monetary system. If something like this was done today, government would tear your hut/house down for refusing to pay your taxes or not getting a permission to build a home at all or some other bullshit reason. If something like this was done in an ancap society, nobody would directly attack you, but you lifestyle would quickly become impossible, as industry and business would sooner or later spread up to your habitat, chopping trees down for resources, building large factories which will pollute the air and scare the wild animals away etc.
Sure, you can say that is a violation of the NAP, but whomever is building a business there can say that the forest is not your private property, and therefore have a right to build a business there.
Of course, you can just move away to another rular area, but the history will repeat itself.

What this essentially means is that you have to be a part of the society, whether you like it or not. That is what I meant when I said economical slavery.

Corporatism can only be achieved by monopolies, but there was never a single monopoly not caused by government meddling in a private sector. If you look at things like the railroad industry, NY Stock Exchange etc, it was all unfairly boosted by the state and so the companies received large numbers of power because of that. That's not Capitalism or Ancapitalism. It's crony capitalism. That goes against any free market idea.

A house in a secluded area would still count as private property if you just got a land permit (Which would be easy to get in an Ancap society) and have that insure the NAP is not violated.

I see your point. Corporations require crony capitalism (which requires a government) to be formed. But here's the problem: if an ancap society gets formed, corporations will still exist. There will be no reset button for them. Yeah, the playing field gets equalized and the corporations become regular companies like any other, but they still possess large amounts of money, and are therefore in a big advantage compared to other companies.
If an ancap society gets formed, Microsoft will still be the top IT company on the planet (alongside Apple), and none will be able to come close to it.
Also, governments may no longer exist, but it's possible for two or more companies to join forces and create a monopoly. Sure, you may argue that's crony capitalism as well, but the companies do not violate anyone's rights nor the NAP if they join forces or merge into one large company, so nobody has the right to complain.

I don't think you understood my analogy about living in the wilderness. Nobody will directly atack you or your property, therefore the NAP will not be violated. But I've explained already in the previous reply as to why that lifestyle would not be possible. Not for a long time, at least. And if you complain, nobody will listen to you. They will call you a luddite, a barbarian or just plainly a lunatic.

And finally (and this is not an argument in favor nor against ancap), I have a question: What will be with the banking system in an ancap society? Banks are without a doubt at the top of the present-day financial and economical hierarchy, possessing large amounts of money, and having many people (nations even, in some cases) in debt to them. Free market does not seem possible with them around.
And as soon as they form a group of hired mercenaries to advocate and protect their interests (something they can easily form with the money they possess), we'll get an entity no different than government.

The crucial thing to note is that the people would be the consumers paying for the companies' products, so if the people don't want monopolies they could vote with their money. Corporations that were once big front runners in their industry have fallen to other companies that started much smaller than them and it could easily happen again.

What would stop you from just getting a piece of paper for the land? It won't really affect much.

Banking would still be a thing. It will just all be privatized. I also think my point about companies being forced to work in the interest of the consumers apply's to you're final sentence in your last reply. Remember, a society that runs off of Anarchism only works when everybody agrees it does.

watch out guys the communism under stander has logged on!

Marxist Leninism believes in a worker owned state capitalism (dictatorship of the proletariat) to eventually be state socialism then communism (a stateless, money-less society)

The state owning and controlling everything isn't communism and is just a part of the transition state towards communism.

Anarcho-Communism rejects that a need for a proletariat state to exist to overthrow capitalism and act towards eventually achieving communism needs to exist and instead believes that there should be no hierarchies or leaders and that the people should organize and have communism straight after the revolution, Anarcho-Communism is actually "True Communism" (a stateless, classless, money-less, hierarchy-less society)