It won't be a problem for me if a police/immigration officer asked me to show my ID/BRP card to check if I'm a legal resident here, whether if they just saw me walking down the street or anywhere else and wanted to ask me about being here because I don't look like British. That should be expected if you're an immigrant, especially if you aren't British citizen yet (it was like that when I lived in Singapore, I was even asked to show my work permit ID when I was buying a prepaid/pay as you go sim card from a store or going to a clinic for a check up, it wasn't a problem for me). No need to cry out the racist remark as long as they're just making sure I have a legal right to be in this country. I'm legal to be here and would never have a problem proving that. Like what Graham said, it should not cause any fuss if you're not an illegal immigrant. The "racist" word is really overused in this country, to be honest. Everything you say or do would always have a possibility of being tagged as racist.