That makes sense to me. These days “Caucasian” means light skinned + white features. I feel like many people still say Italian, Irish, etc. if that’s what they mean.
And yes! I think it’s okay to ask if you’re curious. But I do feel like it matters too much and I’m not sure why it’s of interest to most people. (For example, it’s generally considered rude to ask mixed race people what their races are.)