I have been spending days (on the phone with Apple…) trying to solve this issue. I have also searched, and while seeing similar posts nothing that I can find to do.
I have used SS for many years with no problem. As soon as I upgraded to Sierra, my Gmail account seems to have problems with Mac Mail if the SS filter is on. It will just get stuck “downloading messages” or “downloading 1 of 8k” etc… or get stuck “moving 1 of 8” or any number of messages.
In addition (and I have seen this but with no resolution posted elsewhere) Sometimes I will train as spam and most things disappear for a second and end up back in the inbox box (grey). All new behavior. Unfortunately it is making Mac Mail , SS currently unusable together, as it is just stuck and not moving or downloading messages.
If I turn off the filter it immediately starts counting up the messages it’s downloading or moving, but I end up with a inbox full of spam. I have installed the latest version and removed and reinstalled the apple mail plugin and rule a few times with no success. Any and all help would be greatly appreciated. I can’t imagine using MM without SS, or I have to give up on MM.