Doesn't that line of thought cause you problems? What gives the government the right to pick and choose what names (if the reasoning isn't based on a particular religious belief?) a parent will choose to give their child? That the government doesn't like it, or finds it inconvenient, isn't a consideration in a parent's privilege to choose their child's name. Actions that are not controlled nor prohibited by law are privileges.
I don't where to draw the line. I suppose the question is: Can a parent abuse the right to name a child? If you want to name your boy Sue, OK; but if you give your child a thousand-letter first name because you know it'll screw up computer registries and you're making a point, is that OK or abusive to the child? I'd give the parents a lot of leeway here, but if a parent names their child F*** Me In The A**hole Jones then I wouldn't object to a court looking at it and asking whether the parents are pulling the child into the parents' protest. I suppose I believe that there is a crossable line in which naming becomes abusive.
For that matter, what makes this a 1st amendment issue rather than a 14th amendment issue? The judge isn't congress, and although the judge stated her reason was religious, what her reason in fact did, was "... abridge the privileges or immunities of citizens of the United States ..." and "... deny to any person within its jurisdiction the equal protection of the laws. ..." Letting you or me pick our child's name, but not those parents, is denying them equal protection.
The parents couldn't agree on a last name, leading the court to become involved. I wouldn't disagree that the judge's ruling is wrong in multiple ways, if that's your point.
It is only a 1st amendment issue if the parents aren't really naming their child to give him a name, but making a statement.
It's a first amendment violation by the judge--the govt. picking a favorite religion. Mohammed continues to be allowed as a name, and I'm sure Buddha is OK too. I've known Thors. The judge is in violation of the law.