Missable. Be forewarned.
Once you've completed the Sweet-P arc, you'll be required to go to Honmachi Station to discover the secret of the ticket stub she left behind. Within the underpass you'll encounter Thorn who will give you an alternative to understanding Mu and the Musicians through the pink door. Choose to enter, as it doesn't impede your progress any if you do.
Do note that this is your only chance to choose to enter. If you choose not to, the door will be hidden and you'll have to play through the game again to access it.