I mean, that's nice and all, but it also seems to fly squarely in the face of human nature, or to insist on ignoring it to make an ideological point.

A few problems:
1> Acutally living in such a world would be a nightmare. Imagine a world where there were no overarching sets of laws, standards, a system in which traveling across state, county, city, neighborhood, even property lines means constantly entering and leaving fluctuating sets of laws. Perhaps here your marriage to a man is recognized, move into an apartment two streets over and you can't co-sign because the apartment owner doesn't like gay marriage, go to the next city over to a hospital and your husband can make medical choices on your behalf, get transferred to a specialist in the next county and now they can't, have to move a few hundred miles away for a great job and now you are a reviled sinner and your employer fires you upon finding out and nobody in town will hire you or serve you. And they only resource you'd have against such situations would be to try and find an area sympathetic enough to your homosexuality that you could buy property and encourage other gays to move there and do the same forming a gay mini nation where you can ensure you are treated with basic decency. Of course that is assuming the home owners in that area don't see what you are trying to do and set a gay quota, refusing to sell to additional gays beyond a certain point. You can think of a thousand other scenarios, but such a world would be hell for any demographic other than the dominant one in the culture.

2> Recourse against those who do cause harm would be difficult if not impossible. Say someone does bash your window in with a brick. What can you do? Well if they are a member of your homeowner's group that all agree to follow certain rules, perhaps you can level consequences against them, but what if they arent? To what authority do you then appeal for recompense? What if someone lives upstream from your community and is horribly polluting your water, but their actions are accepted, even approved of by the community they are part of as their industry benefits the community. What if that community neither needs nor wants your trade/partnership/business, and doesn't care how mad you are? To whom to you appeal with no larger governing body?

3>The Rise of tribes and warlords would be inevitable. At some point the gays would get tired of getting kicked around, town A would get real tired of being poisoned by town B, without larger governmental recourse the choices would be to either suck it up and deal with the status quo, or find some way to force satisfaction from the offending party. Violence would erupt, privately paid for police forces used to protect your community interest would evolve seemlessly into armies, and towns/communities/regions would no doubt erupt into war, with regional warlords absorbing territory.

4> What we have now is, in a sense, anarchy-capitalism. What we are looking at in our world right now, as of this moment, is the current state in a long and complicated series of systems and arrangements that primitive man has made to create greater security and prosperity for themselves. Rules that groups have agreed to live under, leadership and authority that rises naturally among pack animals taken and codified. Any system of anarcho-capitalism that did manage to strike a healthy and prosperous balance would have to essentially evolve something that is functionally the same as government.