Holy SCHIIT!
You did it!
I've been looking for a genuine Keep alternative for years! Lots of them were either too complicated, missing sharing, or just not even close. But you did it. Now one of us can be in the grocery story, while the other is checking what we need. It's perfect. And as things get checked of or on, they keep their order! So we can put them in the isle order of the store and we don't miss things, having to go back and forth.

EDIT:
I tested it all on my own and it all seemed to work great. Then while we're both using it, the shearing stopped updating. Every time we reload the page it checked and unchecked items get reset.
Android and Desktop, Firefox everywhere.