Dennis Hopkins was convicted of theft 25 years ago in Mississippi and has long been out of prison. He has raised a family, built a towing business and coached local youth sports teams. There is one thing he hasn’t done: vote. Now he is the lead plaintiff in a class-action case challenging the state’s disenfranchisement of people with felony convictions, one of a number of suits that could affect voting rights across the south ahead of the 2024 election.

       “Many of the members of the class permanently lost the right to vote long ago, and for what most would consider to be minor crimes," said Jonathan Youngwood, a lawyer representing Hopkins and the other plaintiffs.

       States have wide latitude to set rules for elections, and restrictions on voting by felons vary considerably. Nearly half the states ban felons from voting while they are incarcerated. Another group of states also restricts voting for people on probation or parole. In 11 states, felons face high hurdles in obtaining restoration of their voting rights and can lose their access to the ballot indefinitely, according to the National Conference of State Legislatures.

       Rules across the nation have been in flux over recent years as litigation and legislative debates have sharpened attention on when and whether to allow offenders to participate in democracy after they have paid their debt to society.

       “The country is this patchwork of incredibly confusing state laws that are changing constantly," said Vesla Mae Weaver, a professor of political science and sociology at Johns Hopkins University.

       Mississippi is home to perhaps the most visible current legal battle. The state has long imposed lifetime disenfranchisement for people convicted of certain crimes, from rape and murder to forgery, embezzlement or bigamy.

       One case challenging Mississippi’s ban as a violation of the 14th Amendment’s guarantee of equal protection recently failed, though two Supreme Court justices—Ketanji Brown Jackson and Sonia Sotomayor—dissented in June when the court declined to review the case. The justices said the state first adopted disenfranchisement rules in 1890 for the discriminatory purpose of excluding Black people.

       Trying a different approach, the Hopkins plaintiffs alleged the state’s ban amounted to cruel and unusual punishment, forbidden by the Eighth Amendment. That argument prevailed with a panel of the Fifth U.S. Circuit Court of Appeals in August. In a 2-to-1 ruling, the court said there was “a national consensus against punishing felons by permanently barring them from the ballot box even when they have completed all terms of their sentences."

       The full court, however, last week said it would reconsider the case with all active judges participating. Arguments are scheduled for January and the outcome is likely to have a direct impact on tens of thousands of state residents.

       Mississippi said disenfranchisement isn’t a punishment at all, but instead is a judgment about who should get to participate in the democratic process. “Each listed crime is serious, probative of dishonesty or poor civic virtue," it said in seeking rehearing of the case.

       Courts in recent years have been home to a number of cases examining voting rights for felons, but the range of litigation has started to broaden and could set new precedent that impacts voters across the U.S., said Jon Sherman, litigation director at the Fair Elections Center, a voting-rights group representing plaintiffs in a case from Virginia.

       “There’s more—and more varied—litigation in this space than there has been in a long time," Sherman said.

       Legal advocates for the formerly incarcerated say their efforts aren’t aimed at helping one political party or the other, but the issue has tended to split Democrats and Republicans along party lines. This year, Democratic-controlled legislatures in Minnesota and New Mexico passed laws restoring voting rights to felons on parole, with little GOP support.

       The U.S. Supreme Court in a landmark 1974 case from California said states could exclude felons from voting. States continue to cite that ruling heavily in their defense. A decade later, the court ruled against a disenfranchisement law in Alabama, on the grounds that it was enacted with a discriminatory purpose.

       Virginia bars people convicted of felonies from voting unless their civil rights have been restored by the governor. Since 2013, governors of both parties had made it easier for some Virginians to have their rights restored through a somewhat automated process, so long as they were convicted of nonviolent crimes, completed their sentences and maintained a clean record. The state’s current governor, Glenn Youngkin, a Republican, changed the rules after he took office last year, requiring people to apply for restoration on a case-by-case basis.

       Now, plaintiffs are challenging both the underlying law and Youngkin’s latest criteria. In one case, two residents and a nonprofit group argue that Virginia’s indefinite stripping of voting rights from felons violates a federal law that set conditions under which confederate states could have their representatives readmitted to Congress. They also allege an Eighth Amendment violation.

       “The stigma of being a convicted felon, it’s a big issue," said plaintiff Tati King, 52, who has never voted after multiple run-ins with the law. He last served an 11-month sentence for a 2018 drug conviction. “How can I say I’m free if I can’t exercise one of my rights?" he said.

       In a second case, a nonprofit group and a voter who applied to have his rights restored allege Youngkin’s rules violate the First Amendment because they interfere with protected political expression.

       The state in court papers said it gets to make the policy call on when and under what circumstances to grant felons the right to vote. “There is no constitutional requirement that States have any specific process, or any process at all, for re-enfranchisement," Youngkin’s lawyers wrote. A spokeswoman for the governor said the state is increasing the efficiency of its rights-restoration process and is considering the “unique elements of each situation, practicing grace for those who need it and ensuring public safety for our community and families."

       Tennessee is facing a suit from the state NAACP and disenfranchised residents who argue the state’s rules for restoring voting rights are opaque and difficult to meet. That case was filed before rule changes in July, announced by the secretary of state, that say people who have completed felony sentences need a court order or proof of a pardon to begin the restoration process.

       Even in some states where eligibility for voting has been expanding, the rules can be confusing. In Florida, voters overwhelmingly approved a 2018 constitutional amendment expanding post-conviction voting rights, but Republican Gov. Ron DeSantis later said felons have to pay all fines and fees before becoming eligible to vote.

       Last year, 20 Floridians were charged with electoral fraud for voting during the 2020 election while allegedly ineligible to vote. But at least some of the defendants said they had received voter-information cards from the state and thought they were eligible. Legal proceedings are ongoing.

       In May, in the midst of these battles, state lawmakers passed a law saying receipt of a state-issued voter identification card wasn’t proof of eligibility.

       “This card is proof of registration but is not legal verification of the eligibility to vote. It is the responsibility of a voter to keep his or her eligibility status current," the new law says about the cards.

       Write to Mariah Timms at mariah.timms@wsj.com