While one can certainly argue that there is little merit in specially punishing that particular mechanism of achieving those unlawful ends, that clearly is not the same thing (or even a similar thing) to a general ban on flag burning.
Titles of laws are rarely accurate indications of their substance.
Does a white college educated young person burn the flag with no consequences, and everyone else gets hit with intimidation ?
Can these actors be unfair and express biases not in the text of the law? Sure. But that's more an argument for policies to address that problem than it is an argument against additional criminalization of a subset of a category of generally already-criminal acts. (And against which, I should add, there are plenty of other arguments.)
Anyone on the left who disagrees with this argument? Re-evaluate your own principles then, in a way that doesn't assume "my values are right and yours are wrong" in the context of a democratic republic.
Then again, why is burning the flag necessarily "hate speech". I would dare say that it's perfectly legitimate way to protest any abuses that are carried out presumably in the name of that flag - like, say, Gitmo or Patriot Act.