On Instagram, Can You Block Someone Who Has Blocked You?by John Lister
Instagram gives you a degree of control over which people can view your photos and videos. A quirk in the way Instagram works means it may be difficult or impossible to block people from viewing your pics if they have already blocked you from viewing their pics. If you can't work around this, one option is to switch your account to private and gain more precise control over viewing.
You can block users only if your Instagram account is publicly viewable, the default option. This means anyone can see your pics unless you have specifically blocked them. To block somebody, search for her profile by tapping the compass symbol at the bottom of the app and typing in her name or username. Open her profile and tap the symbol in the top right corner (an arrow exiting a box on iPhone or three dots on other systems) and tap "Block User." You can tap "Unblock User" to reverse this change.
Once you block somebody, he can no longer successfully search for your account. Unfortunately this means that if somebody has blocked you, you'll be unable to find his account. In turn, you won't be able to access the block/unblock option. This can be particularly irritating if you've fallen out with someone, and he's beaten you to the punch.
You may still be able to get to the block page if you and the other person have friends in common. This is possible because, even if you block someone, she can still see when you have "liked" a photo or video. You can try looking through photos or videos posted by a mutual friend in the hope that you'll see one that is "liked" by the person you want to block. If you do, you can sometimes tap the person's name on the "liked by" list, bring up his profile and block him.
Blocking has limited effect if you only want to stop somebody viewing your pics. If your account is set to public viewing (which must be the case to use the block function), the other person can simply create a new account and view your pics unless and until you block that new account, which could turn into a cat and mouse game. The only certain way to stop someone looking at your pics is to set your account to "private posts" mode, which means only people you specifically approve can see your content. This can be time-consuming if you have a lot of people interested in seeing your content, as they must each request permission to see your content and then wait for you to approve their access.