I want to share the same iTunes library across 3 users on the same Mac

The library file (iTunes Library.itl) can be open by only one incidence of the iTunes application at a time. Since you seem to be very trusting with your media collection you could set it up so each user has their own library file but media are shared. Try this (untested): Go into an account and make a copy of the .itl file and the rest of the non-media files and folders in the shared iTunes folder so basically you have a copy of the entire folder minus media. Copy that folder to each user's account (maybe put it where they would normally have an iTunes folder). Start iTunes while holding down the option/alt key and direct it to the .itl file in the user's iTunes folder. Check iTunes preferences that it is still directing media storage to the shared folder. From this point on each person will have their own set of playlists, etc. because each person has their own library file, but share a common media pool. It does turn into a slight organizational/management situation though. If somebody adds a new file others will have to remember to add the file iTunes places in the media folder to their libraries too because each listing is now independent. If somebody deletes a track and also deletes the file for that track it will ultimately show as a broken link for others.

The iTunes library folder can only be accessed by one user as you've discovered. Your best bet is to keep the music in the shared folder but keep the iTunes library files be local to each user. The downside is when someone adds new music the others will have to manually add it later. The upside is no more logging everyone out plus each user can have their own personal playlists.