You can tell a lot about how sincere someone is about viewing racism as a serious problem by how they react to be called a racist on a regular basis.
If they think it's a normal, relatable problem that they describe as an annoyance or limitation, they're a racist.
If they think "Hey, it really concerns me that this is happening regularly, because I don't want to inflict pain on others for no reason. Maybe I should talk to some people from the offended group, learn why what I said was wrong, apologize, and promise never to do it again", then congratulations! They have functioning people skills.