Both Serbia and Croatia agree that one of them owns it.

Well, that's settled then! On to demolishing people's homes.

If you build your home in the middle of Yellowstone Park, nobody's going to cry any tears when the Bureau of Land Management comes and tears it down. Don't build your house on land you don't own.

If the federal US government doesn't cry foul that's that.

Everybody agrees Yellowstone is part of the US. This would be like part of Yellowstone the US considers part of Canada, while Canada doesn't claim it but manages it.

You’ve described half the legal situation. The other half is that both sides agree the territory is going to end up on one side or the other, and the only reason a decisive claim hasn’t yet been made is that doing so will weaken claims in contemporaneous disputes over different territories.

People are trying to play this off as if Croatia doesn’t “want” the territory, but that’s not really it at all. They don’t want to lose a larger dispute. They’re happy to have the land.

So: yes, this is approximately “building on Yellowstone” levels of silly.

Yellowstone being a national park that is a protected conservation area detracts from the analogy. There will be those who don't feel sorry for you mainly because you should have chosen another wilderness location, not because they believe you shouldn't build a dwelling in the wilderness anywhere.

It deserves to be noted that even people who camp in city parks do have some supporters. That said, people who have the resources to build a solid home with amenities, including electricity and satellite network access, and keep a website running to tell their one-sided story, are not comparable to homeless campers.

People camp in Yellowstone! Nobody builds a house in the middle of Garfield Park. If you did, even the people camping in Garfield Park would probably cheer it getting torn down.

Yellowstone is actually tricky because of how the Wyoming, Idaho, and Federal jurisdictions overlap. There are some people who believe that in the so-called "Zone of Death", it's impossible to be convicted for murder. The only person who has been charged with a felony in a similar region was given a plea deal that was conditional on him not bringing up the 6th Amendment issues

Apparently one of {Croatia, Serbia}. I think we need to consult the axiom of choice on this one.

That's not true. Neither of them claim it.

They don't but they claim one of them does.

Even if using a function of choice made sense here, you don’t need the axiom of choice to know that a function of choice exists in the case of finite sets.

Currently Croatia manages this territory as its own until the dispute is resolved; so while they don't claim that this is their de jure land in perpetuity, they clearly assert (and demonstrate with their actions as seen in this article) that their law applies there right now.

The squatters should attack this in an international arbitration court at considerable cost if they think it's abuse and they have a chance to win.

Lol, no, not even close. First, what do you mean by 'an international arbitration court'? Such courts exist only because (and in the scope of) treaties where countries explicitly agree to be bound such courts, for example, signing a treaty with a clause stating 'disputes for this treaty shall be resolved in this way'. The only thing binding a sovereign is the treaties they "opt in". But Croatia has no treaties with Liberland, and Croatia has no obligations whatsoever to Liberland - the default state is that sovereign may do as it pleases, including 'abuse', war, slaughter, pillaging, etc - except when they, for example, sign a treaty confirming that there will be a border and they agree not to violate your side of border. If it's really 'terra nullius', then everybody, including Croatia, could do as they please, including burning the place to the ground and killing all the inhabitants, and the only treaty that comes to mind that would prevent that is Croatia's obligations with respect to the European Convention of Human Rights (but again, only because Croatia chose to take on these obligations) that would be violated by slaughter.

This is why a key precondition of being a state is recognition and border agreements with your neighbours - without that, the hypothetical state literally has no rights, not even the right to exist.

The two sides disagree on the algorithm used to define the border. Croatia's algorithm gives it to Serbia and better stuff to Croatia. Serbia's algorithm gives it to Croatia and better stuff to Serbia. So neither claims it. But, nor will whoever loses the fight over the algorithm give it up either.

That doesn't mean either side will accept some third party adding another algorithm and set of borders into the mix.