You've long had the option to remove Instagram followers if you keep your account private, but that's something of a compromise. Why do you have to shut yourself off from the outside world just to keep out a few undesirables? You might not have to make that choice going forward. Instagram has confirmed that it's testing an option to remove followers while maintaining a public account. While it hasn't share more details than that, the app informs testers that it won't notify soon-to-be-former followers that you're leaving them behind. Much as with other social networks, that's likely to minimize outrage from people who can't handle the rejection.
It's easy to see why you'd want the option with a public account. You may not want an ex or former friend commenting on everything you do, for instance. And if you've ever seen the creeps that tend to post leering comments on women's Instagram selfies... you get the idea. This won't prevent sketchier types from viewing your feed, but it will relegate them to passive observers.
Instagram has been expanding your control over its experience lately, including choices to mute people you follow and an experimental 'do not disturb' feature. While they cover a range of subjects, the theme appears to be the same: Instagram wants to eliminate the content that might drive you away, whether it's harassment or too-frequent notifications. Instagram is now a mature social network with over a billion users, and it's just as important for the Facebook-owned service to keep users as it is to reel them in.