There is no option to stop that if you share an Apple ID. See the information in Make sure that each family member has a unique Apple ID - Apple Support including the following:
Apple recommends that you do not share your Apple ID. Instead, set up Family Sharing so that each person uses their own Apple ID. This way, your family can share purchases, subscriptions, and more without sharing personal information like email, text messages, or passwords.
If you share your Apple ID with a family member, certain services will treat you as the same person. You might see these issues:
- Apple Music family subscription: Instead of receiving your own membership with your own library, you’ll share a library and recommendations with the other family member.
- App Store, Apple Books, and iTunes purchases: If Family Sharing is ever stopped, the owner of the shared Apple ID will keep all purchases. You might lose access to everything in the account, including purchases you initiated.
- Apple Podcasts, Apple Books: Podcast episodes and bookmarks might sync according to the other family member’s preferences or be accidentally deleted.
- Messages and voicemails: You might receive text messages and voicemails that are intended for your family member.
- Call history: Your recent call history will include any calls made and received by your family member.
- Fitness: You might see Health details, Workouts, and Fitness+ recommendations intended for your family member.