Presumably those who get to own the Moon will have people here on Earth who they love or care about. Following the "this is just how it is" logic, what's stopping a barrel of gun from being pointed at those people?
That will be long enough that by the time it happens, they may not have any connections to Earth.
Plus, back on Earth, you have all the normal limitations of the gun barrel. If Nigeria doesn't like what Brazil is doing in space, Nigeria is still going to find it challenging to threaten the Brazilians doing space work with guns.
And to the point being made here, protesters protesting out in front of SpaceX are going to find it challenging to successfully deploy gun-power against them, because the local dominant People with Guns take a very dim view of violating their monopoly... and, likely, SpaceX (here really just any space company) is already acting with their approval.
The net of the complicated web of People with Guns here on Earth still pretty much boils down to the situation I described. Space exploration isn't going to be done by voting or polling, and the Veto of the Merely Loud (among the other vetos) that is so easy on Earth is going to prove quite difficult to project into space. In space, nobody can read your Earth protest sign.
I won't say there's never been a country that has fought for independence while simultaneously needing global trade for 100% of their food and water[0], but there definitely hasn't been a case of a country needing global trade for the literal oxygen they breathe.
Two moons colonies, one that has farms and one that doesn't, I would expect to have very different prospects.
[0] Though I've never heard of such a case, my history isn't good enough to make that claim. And no, mere famine isn't a strong enough example for this, those can be monstrously catastrophic without being existential.
But, there's prices, and there's prices. Earth history can tell you all about that.
I mean, we're witnessing how this is a continuum and not a binary thing right now, as East and West are decoupling. Will they decouple fully? Doubt it. Will they perhaps recouple someday? Perhaps. Is there a price to this decoupling? Yes, on both sides, but apparently the sides consider it worth it, because it's happening.
Threaten the loonies too much, and they can throw big rocks at Earth.
They'd have plenty of brute mass up there.