Most don't distinguish between BLM movement and BLM lands.
Most of the US population don't much care about BLM lands. At one point back in the '80s there was some change in BLM rules that affected how a lot of people treated them. It's one thing to have a few state parks. It's another when almost any place you go involves dealing with BLM lands--going through them, having them abut your back yard or be just a couple of miles away.
The new rules were promulgated by people that lived in large cities in states with no BLM lands who did it for "the people," mostly in keeping with the views of the people living in the large cities that rim the continent, not the people who actually used and enjoyed the land. In fact, during that discussion the general attitude among the urban deciders was that the uneducated backwards bumpkins in fly-over country and in the boonies really shouldn't have much say. They should just eat their peas as prescribed by the superior, wiser experts who probably hadn't even stepped foot in the state, much less visited the lands being regulated.
Regardless of what a lot of DUers need, there's no good racial angle here--and that's one of the things raising the incident's profile here. The various picayune militias scattered in a lot of these areas aren't new news but old news. Nobody's been shot or killed. In fact, if the building occupied by the "militia" had never existed nobody would care about it in the least. The land is in the middle of nowhere and this time of year not the most hospitable--those who use it can probably continue to use it.
Another reason for the incident being noticed here is that it's anti-government. There's money involved that could go to the government, and government regulatory and legal power that's at play. (I figure that if nothing's done to arrest or punish them nobody's going to defend "prosecutorial discretion" ... Pointing to another cause.)
The only remaining angle is that these are white, fairly uneducated men who are conservatives if not out-and-out racist. Anything done to crush such is a mitzvah, presumably. We fear this kind of person. Not sure why, but we fear them. Personally, I fear chikungunya more, and that only crosses my mind a few times a year.