In the United States Free Speech Jurisprudence, Speech is considered protected (i.e. Free Speech) until proven otherwise. Thus, the burden of proof that the speech is not protected speech is on the accuser, not the defender. It has been widely held that Free Speech means "Freedom to express the thought that we (collective society) hate." While that opinion is in fact, the dissent (Oliver Wendle Holmes, United States v. Schwimmer) it has been the more quotable portion of the decision to that case.
In your examples of "Hate Speech" lets take the most tame of these examples, the burning of the United States Flag. Generally, the Burning of the Flag is a form of protest of the policies of that country... that is, there is something that the government is doing or did that you disagree with and you want to make your opinion known. No one who loves American and/or Americans would ever burn the Flag of the United States Banner right?
Enter two stage magicians, Penn Jillet and Teller, who do just that... in the Bill of Rights no less! The event is one of the most popular parts of their Vegas show, but if you want to see it, I highly recommend watching either the end of Penn and Teller: Bullshit! season 5, episode 8, where they show it in discussion of Freedom of Speech, or in the West Wing Episode "In the Room" (season 6, Episode 8), where they do this in the White House to boot (or the set of the White House used for a TV show... though this lacks the "restoration" part of the trick).
The point of the trick is that, for every reason such a hateful speech can be spewed, so long as no one is threatened, intimidated, coerced, or harmed, the Speech should be protected for that one use of the foul word that requires it. Should we ban the N-Word (yes I know the irony of self-censoring I just engaged in) and lose it's masterful use in works like "To Kill a Mocking Bird", or "The Adventures of Huckleberry Finn", where it's masterful use was to deliver a striking blow to the people who would speak those words against another?
Because the Nazis mistreated the Jews, do we curb our use of those words in "Schindler's List" or "Anne Frank", both of which decried the horrors of the Nazi Regime with unabashed honesty?
In the United States, you can say just about any abominable word you can think of... it is what the context of the utterance, and more importantly, your actions while uttering those words, that determines if it is protected or not... not the word itself.
"Dort wo man Bücher verbrennt, verbrennt man auch am Ende Menschen."
-Heinrich Heine ("Those who burn books, will burn man in the end.")