Good afternoon morganwhy,
Welcome to the Apple Support Communities!
I understand you would like to share the Apple Music Family plan with your parents, but you don't want them to see your music choices, nor do you want to see theirs. Your expectation is correct, if you set Family Sharing in the iTunes Store, and had them join your family with their own Apple ID accounts, then each of you should have an individualized iCloud Music Library. It sounds like you're all signed in under the same Apple ID. With Family Sharing, this isn't necessary, but would explain why everything you do is replicated on everyone else's device.
I'm going to include all of the resources for setting up the Family Sharing, the Apple Music Family plan, and hiding/showing purchases so that you can check to see if these are the steps you took, and also to confirm all of the settings are correct. If after reviewing this information, you need additional help getting your iCloud Music libraries personalized, please reply back to this thread.
Set up Family Sharing
Family Sharing makes it easy for up to six people in your family to share iTunes, iBooks, and App Store purchases, an Apple Music family membership, and an iCloud storage plan, without sharing accounts. When the family organizer turns on purchase sharing, you can pay for family purchases with the same credit card and approve kids’ spending right from a parent’s device. Family Sharing also lets you share photos, a family calendar, and more to help keep everyone connected.
Family purchases and payments
What types of content can I share with my family using purchase sharing?
Hide and unhide music, movies, TV shows, audiobooks, and books
Get an Apple Music Family subscription
Each member of an Apple Music Family subscription gets unlimited access to the entire Apple Music catalog, music recommendations tailored to their personal music tastes, and access to their own iCloud Music Library, which makes it possible for them to listen to their music on all of their favorite devices.
After you set up Family Sharing, you can invite additional family members to join your family group.
After the invitees accept your invitation, each member of your family group will have access to Apple Music.
If you already subscribe to Apple Music, you can change to a Family Membership in the Music app or in iTunes on a computer. Learn how to manage your Apple Music subscription on your iPhone, iPad, iPod touch, Mac, or PC, or on an Android phone.
Use Apple Music on your iPhone, iPad, iPod touch, or Android phone
Happy Holidays!
