To vote in a presidential election, you must be 18 years old a citizen of the USA, as defined in art. 1 sec. 4 of the US constitution. Census should identify citizenship, legal status or ( ahem ) other residency. pollsters should verify citizenship, legal residency to ensure compliance. States are permitted to enact their own voting requirements in elections in that state level, Federal elections are citizens only.
Once (1980) when I lived in Canade a census taker asked if I vote. I said no, I'm not a Canadian citizen, I am a landed immigrant. She asked what does that matter? I replied to do so would impress my idealogies on citizens.
She did not know the laws of her own country.
It is not wrong to prove eligibility to vote.