Any speech can be defined as hate speech if framed in the right way.
Protesting a flag is "hate" of America.
What the second group was protesting was the removal of a statue that they considered to be historically significant. It is a HUGE leap to consider that hate speech. (Underlying motivations may have been hateful, but the speech itself was not).
Once we alow speech to be categorized and some protected and some not, we gave thrown the idea of free speech out the window.
There is no need to protect government approved speech