Q: "Signed In With a Different Apple ID" Alert Pops Up Every Time

I use an external drive to host my huge iTunes Library. I have copied the library on that one drive and put it on multiple drives to share with other computers in the household (and I also have a master copy I keep on a NAS drive that we share).

When anyone connects to their copy of the iTunes library (all of which originally came from my computer) all the iTunes displays the following alert:

I typically press "sync" and then it goes away for the session. But the alert pops up again every time we quit and launch iTunes. Is there a way to resolve this and turn it off?