Call Out the Behavior, Not the Person
Conversations about race and gender inequality crash real fast if one member of the conversation feels attacked (see “Create the Right Circumstances” - people can’t learn if they feel unsafe). For this reason, it is always wise to get specific about pointing out a comment or a behavior rather than the person themselves - e.g. “that was a sexist thing to say” rather than “you are a sexist.” Calling out words and actions is much more likely to start a productive conversation. This Youtube How-to by Jay Smooth is helpful here.
The organization Showing Up for Racial Justice also has some good advice about how to start these conversations. They suggest “calling in” instead of “calling out.” In other words, approach this conversation as a welcomer into the cause of justice, rather than a police officer of casual conversation. This starts with avoiding personal attacks and labels (like “you’re racist”) and continues with a friendly tone and open questions. If you come into the conversation with that welcoming mindset, your tone and word choice will be more inviting, which will encourage the other person to listen.