Is the district court's suppression of speech about a high-profile and highly charged issue of public debate an unconstitutional prior restraint?

QUESTION PRESENTED Petitioners sparked national debate in the summer of 2015 with the release of videos, recorded during an undercover investigation, which raised legal and ethical concerns about conduct in the abortion industry. Public discussion of Petitioners’ videos prompted investigations and legal changes across the country at the federal, state, and local levels. See, e.g., Planned Parenthood of Greater Texas Fam. Plan. & Preventative Health Servs., Inc. v. Kauffman, 981 F.3d 347, 351 (5th Cir. 2020) (en banc). But on the motion of an abortion-industry trade organization opposed to Petitioners’ message, the district court entered (and the Ninth Circuit affirmed) a sweeping permanent injunction against the release of over 500 hours of further recordings, without applying any level of First Amendment scrutiny. Is the district court’s suppression of speech about a high-profile and highly charged issue of public debate an unconstitutional prior restraint?