Why? Why should racial disharmony be illegal? It sucks when people don't like you, maybe they have good reasons, maybe not - but legislating "harmony" just sounds wrong.
Also, why are people allowed to loudly proclaim "white people are evil" loudly, and broadly, without issues - isn't that also racial disharmony?
You can hate on whoever you like, but you can't grab a megaphone, head down to the mall, and encourage other people to hate the same people that you do. I don't know about you, but that seems like a pretty benign restriction to me...
Your example is a misdirection. What you describe is being a public nuisance in a public area, not free speech. I don't want to be subjected to nasty, racist rhetoric in a public space, just as I don't want to be harangued to repent of my sins and "Let Jesus into my life" in the same place. But I support the right of people to be able to express these views in a published form, or in closed spaces such as on a talking tour or in a church. In both cases audiences are seeking to be exposed to these views and are actively going to a place to find them, not having them pushed on them as they go about their ordinary lives.
If people only hear what they want to hear then issues will never be resolved. It’s necessary to hear things sometimes, even if it’s personally revolting or bothersome. Everyone has to deal with annoying people in life and laws won’t fix it.
Where do you draw the line? All of the items in this list (going from least inflammatory to most) could possibly be construed as causing "racial disharmony":
"We shouldn't give special benefits to [minority group] (eg. affirmative action)"
"[minority group] commit x% more crime than the rest of the population" (factual)
"I personally don't like [minority group]"
"We should enact legislation that specifically penalize [minority group]"
"I wish [minority group] would die/get hurt"
"We need to kill/hurt [minority group]"
"Let's go kill/hurt [minority group]"
For reference, the US criteria is somewhere between the last two (https://en.wikipedia.org/wiki/Clear_and_present_danger).
Source? And I don’t mean calling the individual(s) in this case evil – which they are practically by definition – I mean broadly painting “white people” as being evil.
Is proclaiming "white people are evil" racial disharmony? Depends on the context. Is proclaiming "Muslims are evil" and shooting up two mosques racial disharmony? Definitely.
Whiteness is definitely a race. Thus saying "white people are evil" would seem to satisfy any definition of racial disharmony - how can it possibly depend on context? You appear to just be proving the original posters point that these laws are never actually enforced fairly: white people get targeted by hate all the time and the authorities don't care.
But Islam is not a race. There are white Muslims. Thus whatever hatred of Muslims is, it's not racism.
People routinely lump religious hatred under the rubric of "racism" partly because that word has been granted extraordinary power in our society, partly because there isn't a nice short word for "discrimination against certain religions" and partly because Muslim people tend to overwhelmingly come from certain parts of the world originally.
But regardless of why people do it, no logical definition of racial disharmony could cover shooting up a mosque. You'd need some other type of crime for that to be logically applicable. Or you'd need to define in law that Islam is a "race" you can opt in and out of at will.
Because, this far, your point is pure whataboutism decrying an issue that doesn’t exist.
Come back with this argument when someone walks into a church/mosque and mows down dozens of people. Comparing a few trolls crying on twitter that “white people are evil” to Charleston or Christchurch is asinine