How do foreigners / non-Hindus fit into the caste system? Are there caste equivalent attitudes towards Arabs, Euros, East Asians and so on? Or from a different angle, Muslims, Christians, irreligious, etc. Or does the framework not apply to those outside of the Hindu community?
The question you need to ask yourself is "Does this person come from a background that makes sense to my own principles?"
So the answer to the question depends both on the person asking the question and he subject of that question.
Note: You also need to differentiate between "external" world and "private affairs". Most castes in India dont give much shit about caste when it comes to doing business, hiring, casual friendship, offering/accepting services etc. but care about it deeply when it comes to sharing food/getting married/dating/renting private spaces etc.