Interesting. Well, we've moved away from OoM and are using OurGroceries across Android and iOS now with success. With our modest needs for a cross-platform shared grocery list, OG seems to do a great job.
I had an update to OoM the other day and thought that might fix the issue, but alas, OoM will still not retain checkmarks beside the people I wish to share lists with. I didn't think to try signing out and then signing back in again. I may try that just as an experiment and see if that fixes the issue.
Edit: I previously uninstalled OoM. So I installed it again, logged back in, and once I enter a list to add something, then return to a different, shared list, the checkmarks beside the user names are gone again.
So something is still not right on my side of the equation. I don't know if it's Android 5.0.1 or what. But it just seems easier to stick with OurGroceries now which seems to work fine.
When I first started using OoM, support was awesome. But with this latest issue, I've heard nothing back from OoM support. So that raises a question in my mind too. And yet they are still developing the app. Go figure.