I would disagree with that. Courts in the last 100 years have been more than happy to let government come to private arrangements where they "self" censor in exchange for not being targeted. Just look at things like TV networks refusing to show married couples in the same bed or recent treatment of Pornhub in some states.
Maybe it's true for individual speech in the limited sense of them just speaking (not broadcasting)?
The courts have long upheld the government's right to request action from private entities and for those private entities to comply or not to comply per their preference. That's all that happened here, just as what happened when the Trump Admin (and every administration prior) requested action from private entities.
