We had used an app called Our Groceries, so that my wife and I could add items to the same list from each of our phones. I didn't like the way it looked and I had to keep adding myself as a user via email verification every time I reset my phone, so I made a simpler version. Feel free to try it out. It's a duplicate of ours, so don't worry it's safe to play around with. You can add as many user to this as you want and it's as simple as installing the app through your web browser.
Go to the link. Click the Share Button. Click add To Home Screen & give it name it.