You can find the Court’s order, along with Justice Gorsuch’s dissent, at this link. Justice Alito joined Gorsuch’s dissent; Justice Thomas noted his disagreement with the majority but did not sign the dissent. Justice Barrett again did not participate.
The Gorsuch dissent primarily argues that a North Carolina election board settlement approved by a state court usurped the power of the state legislature, although he also analogizes the holding to the one in the Wisconsin case, which involved a federal court and totally different issues (i.e., the power of a federal court, close to the election, to alter election rules to protect constitutional rights). Justice Gorsuch seems to be trying to move the Purcell principle to apply to state agency actions, and that would be an even bigger problem than applying it to federal court decisions.
There are a few reasons to explain why this position did not attract the votes of CJ Roberts or J. Kavanaugh. First, the issue is messier; to some extent the legislature delegated the power to the state agency to enter into settlements. There’s also the timing and reliance issue; many, many voters have already made their voting plans dependent on the deadlines announced in the settlement, and now we are just days away from the election and there would be no other recourse for some of those voters to vote.
Unlike Justice Alito’s statement in today’s Pennsylvania ruling, Justice Gorsuch’s statement does not talk about any post-election action or any segregation of ballots. But segregation of those late arriving ballots might still make sense, for reasons I explained here in the context of Pennsylvania: it would make it harder for the NC General Assembly to declare the election somehow void and try to get around with the appointment of separate presidential electors.
UPDATE: A few people have pointed out to me that it is possible that this was a 4-4 vote, as it would take 5 to grant the injunction, and J. Kavanaugh (or another Justice) did not note his (or her) dissent. Possible.
[This post has been updated.]