According to the FBI, which considers this a domestic terrorist movement, "By declaring themselves 'sovereign citizens,' they [believe that they] are emancipated from the responsibilities of being a U.S. citizen, including paying taxes, possessing a state driver’s license, or obeying the law."
Things like driver's licenses, permits, and even zip codes are seen as "contracts" with the illegitimate US government that cede one's sovereignty. By rejecting these things, you're "tearing up" the contract and freeing yourself.
These beliefs may be nutty, but the groups are quite serious. A 2014 survey asked US law enforcement officials to rank terrorist threats to the United States. They ranked sovereign citizens as the highest threat — with Islamic extremists coming in second.

Will Trump build a wall to keep these nuts out?

Oh, wait—they're already in.

Joe Stracci