Hate speech is not illegal. Incitement of hatred is. This requires disturbing the public peace by inciting hatred, calling for violence or attacking human dignity (a human right in Germany).

There is also no law against nazi symbols specifically. Symbols of unconstitutional organizations are illegal, this is one of the aspects of being a militant democracy. The goal here is to prevent a failure of the democracy in the way it did with Hitler. Nazi symbols are illegal because of that but they're not the only ones. Communist, socialist and jihadist organizations are affected by this as well.