You have full control over the privacy of your public profile. You can even control most elements of your public profile page separately, including who can view your friends, your nonprofits, your comments, your photos, your videos and your ammado giving circle.
To set your profile privacy, click on "Settings" in the menu. On this page, in the menu to the left, click on the “Account & Privacy” heading and then click on the “Privacy” link. This will bring up a page where you can change privacy settings by turning on or off the relevant switch.