How to mute a contact on Instagram
Open the Instagram app on your smartphone.
Go to the profile by searching for them in the search bar or click on the profile's name of the contact in their post.
Tap on the Following button. A window with three options will open -- Mute, Restrict and Unfollow.
Tap on the Mute button.
Now, toggle the Post button to mute all the posts from the selected contact.
Next, toggle the Stories option to mute all stories from the contact.