Mostly they don't? While I'm sure there's probably some crossover I'd generally consider "people who support the right to carry firearms" and "people who support curtailing existing ownership rights" two separate groups, and it's currently quite possible to legally own any of those. They're not available in really significant numbers, but that's mostly due to market forces (who would want one?).

Whether they'd actually serve as an effective deterrent or not is another question altogether, in an invasion scenario your crackpot neighbor who keeps a field gun in his garage or tries to Zerg rush the Hun with his flamethrower is just going to get killed instantly, he's not a combat threat. Absent any military organization none of this stuff is really especially dangerous, and effective guerrilla warfare requires a minimum of heavy ordnance that can mostly be acquired from the enemy. Everyone having a gun as a general cultural practice can make things a bit hotter for an occupier (see: Iraq), but you don't need specialist weaponry to take potshots at any foreign conscript who wanders off base and keep the rest buttoned up.

It's just mostly a moot argument in the States since while the stuff is pretty much useless for all but the most contrived hypothetical, zero problems have arisen from letting people have it so why throw a bitch fit?