You should be free to do what you want, as long as you are not materially harming another person without their consent.
If these adults wanted to change their own names to "Adolph Hilter" and "Aryan Nation", more power to them. The problem comes when you start talking about raising a kid with the name Adolph Hilter. Lets face it, that is going to have a dramatic impact on a kid growing up, right? Imagine going through world history class with that name.
No, you don't have the right to set your child up for a lifetime of abuse. It's as invasive as the government legally requiring you to educate children. Ideally this is something that should never happen, parents are supposed to love their kids and want what's best for them. When that's not the case, someone needs to intervene on behalf of the children. It's not a vague example of how it's "to protect the kids", but a specific example of two kids whose parents obviously feel that their form of political speech is more important than their childrens state of being.
H.