Users that do not have the Append To privilege on the entity should not see the controls to add activities on the entity form Social Pane.

Currently such users can see the controls "Add Phone Call", "Add Task", etc. in the social pane and can attempt to create an activity. They of course get the permissions error message when they try to save the activity record, however that is too late, they have already gone through all the work of typing up the activity details, e.g. Email, essentially they have done the work we do not want them to do.

The exact same scenario works as expected for the traditional associated views. You do not see the controls to create activities if you navigate to the associated views in exact the same test.
We do not want to use the associated views as users like the social pane a lot, and going back to associated views feels like going back to and old version. I hope this can be rectified in the near future.

This was tested on CRM Online 2016 8.1.0.361. on the Case entity Social Pane.