While there is currently no method to hide your publications from certain followers, there are settings you can change to hide your stories from certain users, limit the posts you see, and control whether your posts can only be viewed by your friends or everyone. You can silence some followers, make your account private or block a profile. When you silence people you follow, the number of posts you see on your feed will be reduced. By making your account private, users will be forced to send you a request to follow you and see what you post.
Steps
Method 1 of 4: Share Your Stories with Close Friends on a Mobile Device

Step 1. Open the Instagram application
The icon is pink and features a white camera.

Step 2. Enter your login information if you do not log in automatically
If you don't already have an account, you can create one by clicking on "Sign up". You need to log in only if you have not already logged in automatically.

Step 3. Click on the profile icon
in the lower right corner.

Step 4. Press the ☰ button located at the top right of the screen
A menu should appear on the right side.

Step 5. Select "Settings" at the bottom of the side menu

Step 6. Select Close Friends

Step 7. Enter a friend's username and hit Add next to it
The friend in question will then be added to the list of "Close friends". You can change it in the tab of the same name.

Step 8. Take a photo or video for your story

Step 9. Click on Send to

Step 10. Select Close Friends
This way the story will only be shared with the users you added to the list.
You can also select specific users to send your photo or video to
Method 2 of 4: Temporarily Silence Followed Users on a Mobile Device

Step 1. Open the Instagram application on your device
The icon is pink and features a white camera.

Step 2. Enter your login details if you don't have to log in automatically
If you don't already have an account, you can create it by clicking on "Sign up". You need to log in only if the login does not happen automatically.

Step 3. Select the user you want to hide
You can find users by using the search function or by clicking on a particular username.

Step 4. Click on the… button, located at the top right of the screen

Step 5. Select Mute
You can choose from the following options: "Disable posts" or "Disable posts and story". By silencing a user, their posts and stories will no longer appear on your feed. The user will not be aware of it and you can continue to see his publications on his profile page whenever you want.
Method 3 of 4: Make Your Account Private on a Computer or Mobile Device

Step 1. Open the Instagram application
The icon is pink and features a white camera.

Step 2. Enter your login information
If you don't already have an account, you can create it by clicking or clicking on "Sign up".

Step 3. Click or press the profile icon
in the lower right corner.

Step 4. Press the ☰ button, located at the top right of the screen
A menu should appear on the right side. Read the next step directly if you are using a computer.

Step 5. Select "Settings" at the bottom of the side menu

Step 6. Select Privacy and Security
It is the fifth option on the settings menu.

Step 7. Click or tap on Account Privacy
This option should be at the top of the menu.

Step 8. Swipe your finger across the switch
next to the "Private Account" option.
Your potential followers will then have to send you a request to follow you.
Method 4 of 4: Block an Instagram User on a Computer or Mobile Device

Step 1. Open the Instagram application
The icon is pink and features a white camera.

Step 2. Enter your login information
If you don't already have an account, you can create one by clicking or clicking on "Sign up".

Step 3. Select the follower you want to hide your Instagram posts from
You can find a user by using the search function or by selecting their name in the feed.

Step 4. Click or press the… button
It is located at the top right of the screen.

Step 5. Click or tap on Block
This will block the profile, posts and stories of the user in question.