If these protesters and anti government militias were trained in the same brand of conservative thinking I was raised with, the idea goes something like this- Article 1 section 8 of the Constitution includes the clause that congress has the power
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;
As you'll notice in the sections I bolded, the Federal Government only is described as having lands if it purchases them from the states for the intent to put buildings on them. So the thinking goes that obviously all the land should have been state land originally and that any federal purchase of land for any use other than for building plots is unconstitutional. So obviously by that reasoning national forests, national parks, monuments, or general multi use public lands owned by the federal government are all unconstitutional. If you start from the assumption that the federal government has no valid property right to begin with, its pretty easy to justify not having to obey federal laws regarding that property. But of course this doesn't answer the question of who should get to have the land if not the government. For this, John Locke provides a very convenient answer:
Sec. 30. Thus this law of reason makes the deer that Indian's who hath killed it; it is allowed to be his goods, who hath bestowed his labour upon it, though before it was the common right of every one. ... And even amongst us, the hare that any one is hunting, is thought his who pursues her during the chase: for being a beast that is still looked upon as common, and no man's private possession; whoever has employed so much labour about any of that kind, as to find and pursue her, has thereby removed her from the state of nature, wherein she was common, and hath begun a property.
Sec. 31. It will perhaps be objected to this, that if gathering the acorns, or other fruits of the earth, &c. makes a right to them, then any one may ingross as much as he will. To which I answer, Not so.... But how far has he given it us? To enjoy. As much as any one can make use of to any advantage of life before it spoils, so much he may by his Tabour fix a property in: whatever is beyond this, is more than his share, and belongs to others. Nothing was made by God for man to spoil or destroy.
So in essence, the public lands should be redistributed to anyone who has and can use them without wasting any of it as a result of having too much. So grazing land should belong to ranchers, mining land should belong to mining companies, and nothing should belong to land users who don't do something productive with the land- such as owners who might use land for scenic or conservation values since they would only hold land to allow its productive values go to waste.
Before I go on to discuss why this argument actually feels downright marxist, lets take a few moments to take apart these arguments. First off, the constitution is actually no where near as narrow regarding land use as section 8 makes it sound. Article 4 section 3 states:
The Congress shall have power to dispose of and make all needful rules and regulations respecting the territory or other property belonging to the United States; and nothing in this Constitution shall be so construed as to prejudice any claims of the United States, or of any particular state.
Or in other words, Congress can do whatever it so pleases with federal land and the Constitution can't be read to automatically judge property claims. So the argument that Federal Land other than for buildings is automatically invalid is absurd on its face and I'm embarrassed to say this was the interpretation I grew up believing was true and the interpretation believed by many of my former associates. At the most narrow reading I can imagine as a lay person, the federal government might be restricted in what it can do with lands it purchases from states, but those restrictions wouldn't apply to land that had always belonged to the Federal government in the first place. And that is making an extremely narrow reading of the text. I believe some would accept that reading, but argue that all federal lands originally belonged to the states originally anyways so how could there be any valid federal land from any other source? Well, there is a lot of complicated legal history that would go into answering that fully, but the biggest part of the answer is actually from Article 2, section 2 which includes that the President
...shall have power, by and with the advice and consent of the Senate, to make treaties, provided two thirds of the Senators present concur...
Most of the territory of the United States was obtained by treaty, either by outright purchase and/or as the conclusion of a war. Such lands weren't state lands to begin with, they were federal. Later states were created and state lands were granted to the states according to whatever deal was written into the enabling act allowing the creation of that state and according to whatever legislation congress passed to dispose of or keep federal lands in that state. Early in history the attitude was to give away lands as much as possible. Later congress and the country changed their minds and the default position was to keep federal lands federal. Due to many factors including the relative fertility of the land and absurd assumptions about how rainwater worked this meant that the western United States is mostly made up of federal land. While this might feel unfair, it isn't unconstitutional and it isn't a land grab conspiracy. As much as anything, its an accident of history.
As long as I'm tearing apart the constitutional theory about why Federal land is supposedly unconstitutional, I might as well give a side note regarding John Locke's property theories. The anti government militia in Oregon provide an excellent example as to why John Locke's theory might sound nice on paper but have less to say about real life. The ability to use property throughout history has not been limited by the possibility that excess property would go to waste. Instead the ability to use property is largely determined by your or your ancestors ability to use force to capture and defend that land. Thus, American Indians don't have many land rights even though in a perfect world most of the USA might still belong to them. So while the Oregon militia might have been thinking in terms of high flying theories, in practice they claimed the ability to use the land by force of arms and have lost that ability because they don't have the political or military power to keep what they seized. A labor theory of property ignores the messy history and by default awards property to whoever had more guns in the past.
In any case, why does it feel like to me as if these protesters are wannabe Marxists? Well, lets trade roles for a moment and see what would happen if I tried to make similar claims about situations in my own life. Lets just say that I decide that the property of my employer should be jointly owned by the sum total of the employees to have made the business productive over the years. So I grab all my weapons and a group of friends and coordinate attacks to seize control of the buildings and property. Because don't you know, the means of production should be owned by the workers not some fat capitalist whose money comes from an unjust system of taxation designed to benefit the rich at the expense of normal people (which is just about as twisted of a half truth as the idea that federal lands are unconstitutional). Then I put out claims on social media asking all of my friends to take over all the local businesses in their area to do the same. Then I start threatening the lives of any local government officer whose official duties might involve disagreeing with me. You wouldn't call me a freedom fighter, you'd call me a communist rebel. But somehow because these protesters talk about the constitution a lot and are scared about how their ranching livelihoods might disappear in a changing economy they portray themselves as freedom fighters fighting for the right to seize government property. Even though I understand a lot of where they are probably coming from, they still sound like wannabe Marxists to me, trying to force ownership of the means of production into the hands of the working class. If they care so much about the constitution, then they need to follow the constitutional process for how changes in government land management are done, that is, through congress. If congress so wishes to gift or sell these lands to them, so be it the Constitution was followed. Refusing to obey the laws regarding your grazing lease, seizing property with guns while wandering around town threatening to burn down the homes of BLM employees, threatening the life of the sheriff's wife and parents, or threatening that all your militia buddies are going to come mow down anyone who opposes you just doesn't count as pro-constitution freedom fighting. It's domestic terrorism.