Sharing Contacts with Family Share

You can try iCloud Photo Sharing.

Photo Sharing - iCloud. https://support.apple.com/en-us/HT202786

Contacts sharing requires use of a 3rd party app/application.

If you want to, you can send Apple feedback. They won't answer, but at least will know there is a problem or a suggestion for change. If enough people send feedback, it may get the problem/suggested change solved sooner.

Click here to send Feedback https://www.apple.com/feedback/

You can accomplish this but it's not an Apple supported solution which means it might/can break other features.

The short version:

If you have a third Apple iCloud account you can add it to both of your devices and turn on Contacts for the account. Set this shared account as the preferred "save to contacts" account for your contacts in Contacts Settings on both of your devices so when you create or change contact info it appears in the shared account and not your non-shared Contacts.

The major issue is the "me" card. iCloud gets confused if you have your "me" card inside a shared iCloud Account! Whomever is logged into this shared iCloud account for Contacts has to keep their "me" cards out of that account and on their own iCloud account.

RULE#1: No one who is logged into the third iCloud account may have a "me" card in that account!

These are the gotcha's that I know of:

1. This seems to break the sharing of WiFi credentials with people who are in your Contacts... at least for me.
2. If you let Siri suggest changes to your contacts it will add those changes and contacts to your personal iCloud account breaking Rule #1 above and causing havoc. Turn off Siri suggestions for contacts.

I have been doing this for 5 years now and find it works pretty well.

This page explains step by step, but is no longer up— there is an internet archive page for it.

And a PDF showing the setup.

Good Luck.