Yesterday, the U.S. Supreme Court by a vote of 6-3 refused to grant an injunction pending appeal in Dunn v. Austin, (Docket No. 21A599, April 18, 2022). Justices Thomas, Alito and Gorsuch would have granted relief. At issue was a suit by an Air Force Reserve officer who has religious objections to the COVID vaccine. His request for a religious exemption from the military's vaccine mandate was denied. The history is explained in the officer's Emergency Application for Injunction Pending Appeal:
[T]he district court denied a preliminary injunction and an injunction pending appeal. While the motion for a preliminary injunction was pending, respondents removed applicant from his command; he does not seek reinstatement to that post, but seeks only protection against further punishment, including a discharge, because of his religious beliefs. After entering interim relief, the United States Court of Appeals for the Ninth Circuit denied an injunction pending appeal in a one-page order over a dissent by Judge Bade.
(Full text of district court's ruling and the 9th Circuit's decision.) New York Times reports on the Supreme Court's ruling.