Tips for accomplices: Turn your curiosity into a compliment. I cannot count the number of times that a white person has asked me: "What are you?" This question often comes after I have spoken Spanish. What you really want to know is how I speak two languages fluently. Turn this into a compliment: "Wow, that's so cool that you speak two languages so fluently. I'd love to hear more about your story."
Self-care tips for folks of color: Ask for what you need at work. If your need cannot be met, move on! There are plenty of organizations looking to hire you.