As usual this thread is also full of arrogant answers by perceived "experts" who are giving less than a minute of thought before typing their responses. How exactly is sharing a link to Apple Music track is violation of copyright? What do you mean when you say "rights to share"? How do I attain that? Apple Music's own share system allows me to copy links to individual tracks, albums and playlist, sharing it with a fellow Apple Music user is a violation? Where is it written?
You have no idea how good this feedback can be for Apple. Spotify has great integration with Instagram for long, that allows "sharing" music right from Spotify to Instagram stories with rich content and custom UI. Apple Music could benefit from the same, as people love sharing what they are playing. Instagram also has a "Music" option in their story composer which apparently is not rolled out to all regions yet and that's why we are getting an error from Instagram, and that is the correct answer for OP.
But looking at the responses here, all this discussion is falling on deaf ears.