Voter registration already does that.If they think that costs and other associated burdens are holding back poor and minorities from voting, they should go door to door and help them get registered, or some anonymous donor can start a foudnation to fund voter registration for poor people.
But people who are not citizens should absolutely not be allowed to vote under any circumstances, and not having a voter ID law to enforce this because of political correctness is madness.
This is not a citizenship enforcement, because it allows ID that is not evidence of citizenship (driver's license and gun license are not evidence of citizenship, non-citizens can get those). A Native American Tribal ID is evidence of citizenship, but isn't accepted. Technically, some non-citizen nationals can obtain a US passport, which is accepted as well. It will only be clear on page 24 of the passport that the holder is not a citizen.