At least payment providers can plausibly point to financial risks and legal concerns as why they engage in what comes off as moral policing. It's pretty clear that any similar claim on HE's part would be pretextual.

>It feels like private companies are de facto writing the laws about what's allowed online and in society right now, and that it's almost become a loophole for censoring free speech on a whim.

"Feels like"? This is clearly embraced as a necessary step to preserve democracy by a small-but-powerful segment of population.