Um, were you under the impression that people don't have the right to be racist? Because they totally do. At least as far as the legal definition -- you will NOT go to jail for being racist, or saying racist things (i.e. my race is better than your race).
There's a legal gray area when you start advocating things like killing "undesirables" on sight, because that is an incitement to violence and does not fall under legally protected speech.
Still, racism is rather frowned upon in most circles, so you can look forward to backlash from people when you show yourself to be racist -- anything from people telling you off and/or distancing themselves from you up to and including losing your job (especially if you are in a position to affect the public "face" of the company, because you better believe that a company's public relations are far more important than ANY single employee).
There's a difference between a legal right to do something and what most people consider to be acceptable behavior, and people are frequently confused about that. The litmus test is to ask yourself whether you can go to jail or be fined for doing something, and whether that's applicable only to a narrow set of circumstances or across the board. If you won't get into legal trouble for it, you have the right to do it. It just may be inadvisable to do so.