It is not possible to view Instagram stories anonymously while using the Instagram app or website as it requires you to be logged in to view content. However, there are third-party apps and websites that claim to allow you to view Instagram stories anonymously.
However you can view Instagram stories and post of any public profile at storyglance.com
How it works:
1. Write username of any profile in the search box, then hit the button.
2. You shall see any available story and all posts of that profile.
3. You can add the profile to your favorites, so that you don't have to search next time.
4. Also works for post links.
