With respect that is crap. The law and everyone else is perfectly capable of discerning people preaching hatred from people demonstrating for their rights.
They sure
seem like they are, banning Booberry dresses in France, and swastikas in video games. That's completely rational and necessary to maintain societal order. Except it's not: it's state-sanctioned enmity with Islam and petty self-flagellation over the crimes of people mostly long dead, respectively.
But really, that highlights the problem: in a democracy, or any human system, discerning people are not necessarily or even often the ones who achieve power. Thus when discerning people do have the temporary advantage, they frame laws defending the minority from the majority which are then made very difficult for the majority to change.
If you don't have a fundamental law that recognizes the freedom of Nazis to march, there is no fundamental law that recognizes anyone else's freedom to do so, either. All you have is a privilege, revocable at any time by an adversarial legislature, not a right.
Beyond that, silencing any speech or merely expressive conduct is so deeply offensive to human dignity that no government should have the power to do it. It's as basic to liberty as the presumption of innocence or the right to take part in the political process.