How to use different contacts on different iPhones with the same Apple ID
The only reason I can see for sharing an Apple ID is to share purchases.  Otherwise as you have found out, you are sharing contacts, calendars, emails and maybe even video calls and imessages etc.

Luckily, whilst all the above are iCloud functions, they are not mapped to your App Store account, and you can sign into separate accounts for each of these functions on your device.

So, on the assumption that the above is your scenario, then just sign into the App Store with the existing Apple ID which then is only responsible for purchases and download authentication etc., and then one of you can sign up for a separate free iCloud account to handle all the other functions.