Android - Can I share Google Keep notes between people?

Currently there is no way to share notes on Keep in the same way that you can share a document.

However, if your goal is to share notes between a fixed amount of persons (e.g. family members,) you can always create a new Google account, add it to all Android phones that you need to share on, and enable sync of Keep only on that account.

As of now, yes:
Google Keep: Share ideas with friends and family

Each note now has a share button you can use to share it. More info:
Share & collaborate in Google Keep

Try Wunderlist, they have a great IOS and Android app that does it. I know some people who use it and they really seem in love with it.