Well, certainly companies have been successfully sued under civil rights laws, and racist language used by an employer, for example, can be evidence of violations of the civil rights act. You can't discriminate based on race, and use of racial epithets can be evidence of such discrimination. A discriminatory work environment is not protected by the Constitution. It's the discrimination that's illegal.
Or, for example, a racist employer may be sued by an employee for harassment or unfair treatment under employment discrimination laws. But in these cases, it's not the racial language itself that runs afoul of the law, it's the harassment or discrimination. If you're subject to racial abuse at work, that's harassment...but the same would go for any other type of harassment.
The have been numerous such cases over the years, some with significant damages awarded. The fact that certain speech is protected under the Constitution doesn't grant blanket civil immunity from other illegal actions. Just because it's not illegal to call someone an "old fat" for example, doesn't mean you can engage in age discrimination.
I'm not aware of an instance of a private employee, in his or her individual capacity, being "fined" by the Government solely for using a racial slur. There's no law against racial slurs per se. But again, if complaint was related to some kind of harassment or discrimination, the racial slur would certainly be evidence that such harassment or discrimination was occurring however. But in any event, no employer has ever been sued or sanctioned by the government for running afoul of "hate speech" laws, because such laws don't exist in the US.