Currently different modules use different logic to determine whether they should appear on the My Moodle page. For example the assignment requires a due date and must be accepting submissions. I think it should be an explicit setting for the activity module to allow hiding it from My Moodle as it is currently unclear.

Hide from My Moodle [x]

This would require changes to all modules as it would also be confusing to only support this for some modules and not others.