I smell a Constitutional challenge.
Do parents have a right to name their children anything they like? I'd argue that they do not. The First Amendment doesn't say that you can say or do whatever you want, whenever you want, without the slightest regard for the consequences of such action. Consequences are always a relevant legal consideration, hence the classic example "you can't yell 'FIRE!' in a crowded theater."
The father concedes that his particular brand of attention whoring has brought death threats.
The Campbells insist that they selected their kid's Nazi-themed names because those names were "unique" and honored their German ancestry. That may be true (it isn't), but it casually ignores the contempt such names draw upon the bearer, compelling children to bear, at a minimum, the near-universal derision of the parents' politics.
It is difficult to ignore the fact that the parent's names are the utterly ordinary Heath and Deborah. Obviously they didn't believe strongly enough in the importance of their unique German ancestry to change their own names to something Nazi-themed. Nope, they chose to foist that crap on their children.
That's not "protected speech." It's just irresponsible parenting and a cowardly form of attention whoring.