StealthPeek

StealthPeek is an anonymous Instagram viewer. Enter any public username to watch stories and posts, see followers, tags, comments, and download media in original quality. No login is required, and your name never appears in the viewer list.

All activity runs through StealthPeek's servers, so your identity never reaches the profile you're viewing. It works in any browser, is updated as Instagram changes, and only accesses public profiles. Private accounts are out of scope, and the site explains safe, legal use clearly.