how can a local cop arrest me if I'm not breaking the law?
Well, he would slap handcuffs on you, say "you're under arrest, these things are illegal!" and haul you off. Then, days or months later, when somebody who knows the law (or knows enough to bother looking it up) looks at the case, they will say "you dolts arrested this guy for a legal gun!". Then the charges will go away and you will get your super awesome gun back.
You are right, they are wrong, but that won't always keep you out of trouble. Particularly if you have an attitude and try to preach/screech at dimwits who think your sweet sweet rifle is illegal/improper/needs a permission slip from the pope.
Find a range that is familiar with NFA items or go shoot in the swamp (or on the ocean, I think there's a bit of water down there).