This morning, the Supreme Court decided Husted v. Philip Randolph Institute, overturning 5 to 4 the Sixth Circuit decision that invalidated one of Ohio's voter registration list maintenance procedures.  Justice Alito wrote for the Court, starting by clearing stating the facts at issue, which have been politicized into slogans like "Ohio's voter purge" by the left throughout this case:

At issue in today’s case is an Ohio law that aims to keep the State’s voting lists up to date by removing the names of those who have moved out of the district where they are registered. Ohio uses the failure to vote for two years as a rough way of identifying voters who may have moved, and it then sends a preaddressed, postage prepaid card to these individuals asking them to verify that they still reside at the same address. Voters who do not return this card and fail to vote in any election for four more years are presumed to have moved and are removed from the rolls. We are asked to decide whether this program complies with federal law.

The Court found that Ohio's practice is in compliance with the National Voter Registration Act (NVRA) (internal citations omitted): 

Respondents argue (and the Sixth Circuit held) that, even if Ohio’s process complies with subsection (d), it nevertheless violates the Failure-to-Vote Clause—the clause that generally prohibits States from removing people from the rolls “by reason of [a] person’s failure to vote.” Respondents point out that Ohio’s Supplemental Process uses a person’s failure to vote twice: once as the trigger for sending return cards and again as one of the requirements for removal. Respondents conclude that this use of nonvoting is illegal.  

We reject this argument because the Failure-to-Vote Clause, both as originally enacted in the NVRA and as amended by HAVA, simply forbids the use of nonvoting as the sole criterion for removing a registrant, and Ohio does not use it that way. Instead, as permitted by subsection (d), Ohio removes registrants only if they have failed to vote and have failed to respond to a notice.

While the decision is largely one of statutory construction, it is also one that respects the proper role of the court and defers to the lawful policy judgments made by legislatures (internal citations omitted):

Requiring additional evidence not only second-guesses the congressional judgment embodied in subsection (d)’s removal process, but it also second-guesses the judgment of the Ohio Legislature as expressed in the State’s Supplemental Process. The Constitution gives States the authority to set the qualifications for voting in congressional elections,  as well as the authority to set the “Times, Places and Manner” to conduct such elections in the absence of contrary congressional direction. We have no authority to dismiss the considered judgment of Congress and the Ohio Legislature regarding the probative value of a registrant’s failure to send back a return card. . . .

It is not our prerogative to judge the reasonableness of that congressional judgment . . . . The dissents have a policy disagreement, not just with Ohio, but with Congress. But this case presents a question of statutory interpretation, not a question of policy. We have no authority to second-guess Congress or to decide whether Ohio’s Supplemental Process is the ideal method for keeping its voting rolls up to date. The only question before us is whether it violates federal law. It does not.

Justice Thomas wrote a concurrence to raise constitutional concerns with the respondents' view of the NVRA (internal citations omitted):

I join the Court’s opinion in full.  I write separately to add that respondents’ proposed interpretation of the National Voter Registration Act (NVRA) should also be rejected because it would raise significant constitutional concerns. . . . As I have previously explained, constitutional text and history both “confirm that States have the exclusive authority to set voter qualifications and to determine whether those qualifications are satisfied.” . . . Respondents’ reading of the NVRA would seriously interfere with the States’ constitutional authority to set and enforce voter qualifications.

While the left will hyperbolically decry this decision as promoting voter suppression, Ohio's process has many protections to prevent voters who still live in the state and wish to remain on the voter registration rolls from being removed.  That is why the Court correctly upheld the practice under the NVRA.  As Justice Alito noted, difficult policy judgments about the best ways to administer elections, protect the integrity of elections, and ensure that every eligible voter is able to vote should be made by legislatures, not by unelected judges.