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).
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...