Photos is a single-user application. If two users are using the same Photos Library, you will run into permission problems, if both users are modifying the library. One way to prevent that is to move the Photos Library to an external drive or a separate disk partition. This way you can enable the "Ignore Ownership on this volume" flag. The method is described here for iPhoto, but will work also for Photos: iPhoto: Sharing libraries among multiple users
Added: I am just seeing Larry's reply:
The "Ignore Ownership" method is working for me, as long as the Photos Library is not an iCloud Photo Library. That would be problematic with two different AppleIDs.
And sharing the library in iCloud will not work at all, if the user accounts are using different AppleIDs. Apple's recommended method for sharing are Shared Albums. Share selected photos in iCloud, but not the complete library. iCloud: iCloud Photo Sharing FAQ