Could it perhaps be the case that a hypothetical white writer who was fired for using the n-word in a business setting where black people were allowed to use it and frequently did so would have a legal case due to equal protection?

I’m not sure a policy that forbids certain speech by speakers based solely on race is legally defensible, but ianal.

*edit to add* Obviously the actual verbal/linguistic context matters for the harassment potential for various acts of speech, but I’d argue that the restriction on the n-word from white speakers in most corporate settings is absolute; ie a white person can face potential consequences for quoting it, calling another *white* person it, or even saying it or it’s analogues by accident eg the mlk coon slip weatherman incident). All this is simply to point out, it’s simply the word and not its verbal/linguistic context that matters when whites use it in many contexts, so it would be hard to launch a defense for a double standard policy towards black corporate usage that is verbal/linguistic context based. Black linguistic usage is largely in nearly the “worst” possible linguistic context for white speakers, ie to refer to generic black people, so the only “mitigating” context is race, not linguistic context.