Hi,
If you are having issues with accessing the shared Subscriptions, and no one else is, I would recommend leaving the Family Sharing and rejoining.
On your device, go to:
Settings > Name > Family Sharing > Me > Leave Family
Once you have confirmed you are no longer tied to the FS, have the organizer send you another invite via iMessage.
On the Organizers device, go to:
Settings > Name > Family Sharing > Add Member > Invite via iMessage > click on the link > rejoin the FS.
Once you have rejoined the Family, go to Settings > Music and confirmed Sync Library is enabled as well as Automatic Downloads.
Attempt to access and download Apple Music content within the Music App, as well as as the News+ App.
This should resolve your issue.
https://support.apple.com/en-us/HT201088
https://support.apple.com/en-us/HT201088
https://support.apple.com/en-us/HT204926
https://support.apple.com/en-us/HT205595
Hope this helps!