I have a Webstagram (an Instagram viewer) account, since I don't have an iOS device, and some people that follow me have private profiles, so I can't follow them back.
Is it possible for me to follow them back? And if yes, how?
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Instagram restricts private profiles to only those who have an Instagram account and have been authorized to view.
Private media is returned as long as the authenticated user has permission to view that media.
Considering this, it's not possible to follow them back.
A dirty workaround (which doesn't precisely answer your question) could be as follows.
Borrow an iOS device from your friend for several minutes. Install Instagram (or log out if it's there already). Register an account with Instragem; add those friends who have private profiles. Log out again; return iOS device. You need to do it only once in your account's lifetime.
Looks like from that point, you'll be able to log into WebStagram with newly created Instagram credentials, and to add public users to your Following. And the desktop web version of Instagram seem to also allow you to add private users to Following.
In my experience I have just clicked on "Follow" button when their profile is private. If the person knows you or not they will approve the follow.
Majority who are on Instagram I've noticed have public profiles.
If the people who are following you are ones you know then that's good but if they aren't then delete them. You also can set your profile to private.