Sometimes your clients not interested in using the Activity Feed Posts functionality in Dynamics. You can turn it off system wide in two simple steps. Firstly go to Settings -> Activity Feeds Configuration and filter all the Active records and Deactivate them.
Now goto Customization -> Default Solution and Publish all Customizations. You could do it for each entity if you prefer.
Once you refresh your browser cache the Posts tab on the activity pane will be hidden.