By default, only users added to your MyFitnessPal Friends list can see the activity on your news feed.
The only exception is that a user's News Feed will show the comments made by their friends on the updates of other users. The update the friend is commenting on will also be visible in the user's News Feed for context, even if that user is not one's friend.
In general, however, your activity will only be shared with the people that you trust and want to support you. If you don't want someone to see your activity, simply remove them from your friends list, or don't add them in the first place.