If you care about privacy, these are the Google Keep alternatives to switch to
(www.androidauthority.com)
For shopping lists I use Listonic. It's easy to use and better suited for shopping because it groups products into categories, so you don't have to sort them yourself and don't have to walk around the store back and forth because you picked up strawberries, moved to the toilet paper section and diary and then noticed you didn't pick apples. :) It syncs, so if you go shopping with somebody else, you can split and see what the other person already grabbed (as long as there's connectivity, of course).