Hello Pierogas,
If you're describing your family members not having access to the playlists that you have created within your Apple Music library, then that is expected behavior, as each family member will have their own Apple Music library and should be using their own Apple ID with Family Sharing.
You can see that outlined here:
And each family member gets their own personal music library, and music recommendations based on what they love to listen to.
Playlists can be made public, and followers can see and listen to it via Apple Music, however that is not a feature of Family Sharing. You can read those details here: See what friends are listening to in Apple Music on your iPhone, iPad, or Android device - Apple Support
See what your friends are listening to
To see and play music that your friends are sharing, go to Listen Now, then scroll down to Friends Are Listening To.
To see a specific friend's profile, go to your profile, then tap their photo under Followers or Following. From here, you can see their shared playlists and what they're listening to.
If that feature, or if playlists from the Apple Music library aren't available for your family members, then reach out to Apple Support directly to help investigate the unexpected behavior. They'll have the tools necessary to help resolve the issue.
You can reach them by clicking here: Apple Support or calling the most local number in your region: Contact Apple for support and service
Cheers!