It is against U.S. law for the U.S. military to enforce local or state laws. That's a job for the police, or the National Guard (but only when acting under state authority).
The law came about as part of a compromise to end reconstruction in the south. We still have it on the books because, among other things, the regular military's mission, training, and equipment makes it a really bad police force.
So why do small towns have paramilitary police units? And don't they make things worse?
Despite the fact that a Department of Homeland Security report once listed more potential terrorist targets in Indiana than New York or California, the state has never been hit by a terrorist attack, much less an assault involving IEDs. The MRAP vehicles amount to only a small fraction of the $45 million in materiel that Indiana has acquired from the Pentagon since 2010. While such detailed findings aren't available for every state, The New York Times reports that 432 MRAP vehicles have been distributed to law-enforcement agencies across the states, in addition to 435 other armored vehicles, 533 planes and helicopters, and nearly 100,000 machine guns.
In a lot of cases, these advanced armored military vehicles are only ever used for parade pieces, Bieler says. That's in stark contrast to SWAT deployments. Peter Kraska, a professor and senior research fellow at Eastern Kentucky University, reports that between 1980 and 2000, police paramilitary teams registered a 1,400 percent increase in deployments.
It is far from clear that a weapon of war is a tolerable answer to civil unrest even under the worst circumstances. Ferguson [Missouri] is hardly the only community where assemblies protected by the First Amendment have been met by paramilitary force. The police reaction following [unarmed 18-year-old Ferguson resident Michael] Brown's death—the latest in the hopeless litany of young black men killed by authorities—shows how far the militarization of law enforcement is spreading.
This is a hallmark of the right, of course. Right-wingers are essentially terrified of their own shadows. They're weak and insecure, which leads them to seek hard power, like guns and military force, in order to feel less afraid. For exactly the same reasons (weakness, insecurity) they have no tolerance of dissent or even peaceful protests. It's up to rational people to tell the irrational ones they can't have these things, because those things make everyone worse off.
Exhibit: After the events this weekend in Missouri, having a heavily-armed police force seems to have made everyone in town less safe. With emotions running this high, and with one side having military-grade weapons, how will anyone have a good outcome?