Allowed to not serve??

I am a gift shop clerk. I was wondering if it's legal for me to not serve someone that comes in and acts and says things that are wildly racist or sexist or things of that matter? Like if someone of a certain race came in and were saying awful things about another or even dared say it to or around someone if the rave they are speaking illy of? Am I legally allowed to not serve them or do I still have to?

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