This is at least internally consistent until you concede some kind of role for the government. And that's the problem militarization presents to the right.
Capitalism implies no upper limit to the police power we invest in the state, but it demands a minimum: at the very least, the state must maintain a capacity for violence superior to the general population. That, after all, is what it takes to enforce contracts, to protect private property, and to deter criminals.
But having conceded this, Capitalists cannot, as they usually do, simply delegate the task of optimization to the market - that responsibility falls squarely in the lap of the government, which must retain its monopoly on violence. And this, of course, is the basic task of liberal governance: exercising the power of the state as responsibly and rationally as possible.
Functionally, Libertarians are using "militarized policing" in the exact same way that liberals use the word "tyranny" - to make a pragmatic distinction between irresponsible and responsible uses of force. As any NRA member will gleefully explain to you, distinctions between "military" equipment and "police" equipment are mostly arbitrary, based on the exact same logic that pinko hippies would use to justify singling out "assault rifles" from "hunting rifles" for regulation. We are not dealing with categorically different types of state violence here - just different degrees. Proportion and propriety can only be evaluated through the hard work of liberal democratic governance.