Instagram has added the ability for users to share stories only with a specific subset of people, not just anyone who follows them.
Users simply create a "close friends" list and then only select specific stories with that group of people. To access the feature, go to your profile in the Instagram app and select "Close friend list" from the side menu. From there you can add your closest friends to the list. Whenever you share a story, you have the opportunity to share it with all or only your close friends.
There are a few things you should keep in mind. First, no one can ask to be added to your list. So there will never be the awkward part someone wants to join your list, but you do not really care about it. Second, your friends know if you've added them to the list of close friends because they'll see a green badge when they see stories you just shared with your list. Your list will not be added and it will not be yours selected stories, and you will not even know they were left out. Savage!