Free baseline
Google Keep

Google Keep is a light checklist beside Gmail.
Who it’s for
The note should sit next to the Google calendar you both open.
Who should skip
Skip it if the cart has outgrown a checklist.

Price
Free with a Google account.
Works on iPhone, Android, and the web.
Last checked
Setup on both phones
- Share one checklist.
- Keep it on the Google account you both open.
What to put in it
- A short checklist beside the Google account you both already open.
- Not a full week of headings and bills.
- Not the cart, if AnyList is already the list.
Checked against Apple Notes
Apple Notes is the shared note when both phones are in iCloud.
The downside
A full week of headings and a branching grocery list will not fit.