To prevent someone that follows you from seeing your activity, you should remove that person from your Followers list.
And what if you want to stop seeing other people's activity? Simply remove them from your Following list and you'll no longer see anything related to this profile.
Finally, your profile is public by default but you can turn it private so that no one can see any of your posts or rounds without your permission.
When your profile is private, other users will not be able to see your activity but they can still request to follow you. Then it is up to you to decide!
Private golfers won't appear in the Leaderboards of the Course Profile section.