>Constitutionally, states cannot deny citizens the right to vote.

Yes they can. States can deny citizens the right to vote for "participation in rebellion, or other crime", as per the 14th Amendment and felons are often denied the right to vote. They can't do so on the basis of "race, color or former servitude" (15th Amendment) and probably not any other protected class reason (sex, religion, ethnicity) but that implicitly gives states the right to do so for any other reason.