The ruling allowed the Trump administration to continue to pursue changes that include enlisting the Postal Service in checking voters against a national database.
Ms. Carroll, who prevailed in a civil trial after accusing President Trump of sexual abuse, is the latest target in a Justice Department campaign going after his perceived enemies.
Republican leaders in the state have asked the justices to clear the way for a congressional map that a lower court found discriminated against Black voters.
A group of immigration judges in 2020 challenged work-related restrictions on their public speaking engagements, saying they violated their free speech rights.
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