If Neil Young's contracts allow him, he is free to choose to stop using Spotify. That's all he said in his letter: Spotify can't have both his music and Rogan's podcast.
Calling this "censorship" is authoritarian.
Censorship has many forms, and is not exclusive to the government. Corporate censorship [1] in response to social pressure seems to be the dominant one in our era.
For example, Spotify doesn't have startup competitors because it's so difficult to get legal rights to streaming. The government could require that music owners of significant size publish prices for streaming rights and apply those prices equally to any streaming service.
I think Spotify is doing the right thing in this particular case (though probably not because of some principled commitment to free expression, but merely for the sake of the bottom-line).
Neil is just saying: "If you're going to do <X> (which just so happens to be patently obnoxious and harmful) -- I don't want to be associated with it. So I'm going to find another party."
Which he has a perfect right to do -- full stop.
