Dual Apple ID Users sharing one iMac w/ continual log in error messages

We are two separate Apple ID users falling under the same family plan of Apple One Premier subscription. However, we are both sharing the same iMac. I'm the primary Apple One Family plan and also an iTunes Match subscriber (as I've opted to have all of my digitized music stored in the cloud).

When I attempt to use Apple Music to listen to purchased, cloud stored music. I get the attached screenshot.

Are there constraints with two users on the same computer subscribing to Apple Music?