Mail not quitting...it's greyed out.

For the past week or two MAIL, although seemingly working fine otherwise, does not quit when I choose quit. I also recently noticed popups about messages appearing on the right side of the screen. These never came up before either. I found a way to turn them off in SpamSieve, but MAIL continues to not quit properly. I “suspect”, but haven’t verified that SpamSieve is preventing MAIL from quitting.

The ONLY WAY OUT is to FORCE QUIT MAIL. Not a good plan.

That seems unlikely, but to find out for sure you could use Activity Monitor to sample Mail when it’s stuck and then post the sample log here.

Test
I will run your test, but after my post I tried quitting SpamSieve first, then quitting Mail second. No problems (but just a single test).

That’s probably just a coincidence. SpamSieve’s Mail plug-in does not know or care whether the SpamSieve application has quit.