Petty & childish. If people want to listen to Rogan then they will. Neil Young is no more a medical expert than Rogan is, so both are essentially expressing personal opinions. I've made the point many times that there is never just one way to look at things. Spotify isn't forcing anyone to listen to those podcasts or any other output (including Neil Young songs).
Van Morrison is another anti-vaxxer who has used his music to express his views. I've seen Van the Man a few times and I'll continue to listen to him, just not this recent output. But I'm not refusing to listen to any of his stuff, deleting any digital content or throwing away physical media of his.
Neil Young is also entitled to his views and if he doesn't want his music on streaming platforms then it's up to him. In fact even before this, there were times when you couldn't get some of his albums on Spotify or Tidal, then they'd appear, then they'd disappear again.
I've willingly had all my vaccine shots, plus flu and pneumonia jabs and there's certainly solid data to show that these are beneficial but that doesn't mean we shouldn't ask questions or ignore potential side-effects. Or even question the whole political handling of Covid over the last 2 years. If Young is so worked up then why not go on the podcast and debate it?
It's like Sally Rooney refusing to have her last book published in Hebrew because of her views on the Palestinian situation. Many who might have read those books would quite possibly agree with her.