Will I lose followers or subscribers in Apple Podcasts if I switch hosting providers?

You won't lose listeners as long as you set up a 301 redirect from your old RSS feed to your new RSS feed. Most modern podcast hosting services will help you with that. Once you're done migrating your podcast to the new host, go back to your old hosting provider and find the location for redirecting your feed. Paste in your new RSS feed URL from your new hosting provider.

If you don't have access to your old RSS feed on your previous host, you can log into Apple Podcast Connect and update your profile with your new RSS feed URL there.