Other trackers may require a set IP for VPNs to work but mullvad doesn’t allow static IPs if I recall. The way around this (from my experience with other trackers) is to set up 2 factor auth. I haven’t used audiobookbay, but this was my solution for 3 other sites.
Yes this was my experience with some websites as well until I set up an account with two factor authentication so that I could authenticate my IP properly. Some of these web servers are set up to deny certain IP ranges that can’t be cached.