I agree that Spotify has the legal right to stop distributing any content they find objectionable. Anyone arguing that Spotify’s action is a first amendment violation is simply wrong. A private entity, like Spotify, can decide what content to distribute at their own discretion. I don’t think many people are making this argument.
Instead, I think many of us are arguing that Spotify shouldn’t exercise that option just because of an outraged online mob. That includes those of us that aren’t particular fans of Rogan and wouldn’t be affected if we couldn’t consume his content anymore. Many of us are arguing that as a general principal; don’t give in to a short-lived and irrational angry mob.
I am arguing for Spotify and other content distributors to ignore angry mobs because I worry that eventually such a mob will come for something I do value. E.g., I listen to plenty of music that includes gratuitous levels of profanity. I imagine that such music greatly offends many people, chiefly culturally conservative prudes. Should such an online mob form and demand Spotify stop distributing some of my favorite music then I hope Spotify resists that mob.
Maybe one day I’ll even be a member of such a mob demanding that some platform stop distributing something that offends my sensibilities. While my emotions of hate and outrage may cloud my rational judgment, I hope the platform will have the courage to tell me and my compatriots to pound sand. If we don’t like the content, then we don’t have to consume it.
*Edited to fix a mistake as pointed out in a reply.