Instagram is reportedly in the works of certain changes, which would now allow people to mute the accounts, to which you are subscribed to. That said, the new feature will let you to mute certain accounts, without unfollowing/unsubscribing them. However, Instagram would not let the person, whose account was muted by you.
The feature comes handy for people, who want to get rid of the stock of notifications hitting their account, when they got tagged in the post/comments section. Users will have the option of muting either the post/story of the subscriber, or even both. Interestingly, Instagram is not planning to limit the number of accounts, which you can mute.