What I'm confused about is why the Purcell principle did not apply here? This is a major rule very close to an election, and SCOTUS has blocked other changes in the past. What is the rationale this time? This seems like a pretty clear cut idea. If you want to suddenly create new requirements to vote (or allow existing ones to go into effect), don't do it just a month or two before a general election.
The 8th Circuit lifted the District Circuit's stay in September - before any ballots were mailed out. They ruled the Purcell didn't apply at that time. The Supreme Court just upheld what was ruled on in September.
http://media.ca8.uscourts.gov/opndir/18/09/181725P.pdfAs to the effect of this, even the District Court acknowledged that about 13x more non-Native Americans didn't have the proper ID at the time of their decision than Native Americans. Given Native Americans' already anemic voter participation rate, requiring a voter ID might actually preclude more Republicans from voting than Democrats.
