Hide Individual Activity

To hide the activity of an individual supporter in a campaign from the public, go to Edit this Campaign for the campaign in which the supporter activity shows up. Click on Activity on the top navigation menu, and open the "Manage Recent Activity" section. Click on edit, and toggle to "Hide" any activity you do not want showing on the public activity feed for the campaign. 

This will hide all the details entirely for this activity. 

If you'd instead like to hide the entire activity feed, see here.