I'm a minority, and have been called racial slurs in past jobs where I had to interact with end-users on the company's public tech support forums.
I would NEVER respond to the people saying that shit, that kind of stuff gets blocked/deleted and you move on. Now if a co-worker in my actual office even so much as displays a SLIGHT hint of racism towards me - I'd send their ass to HR in a heartbeat. But if it's some random fuck on the internet? I would just send an email to my manager like "Hey just FYI there's some racist idiots on the forum, gonna ban them, these are there account #s, thanks" and my boss says "ok, np, good riddance.".
That's how you handle shit when you deal with the public. Don't make a scene of it and make your business look bad, that doesn't help anyone.