Short answer
You can view Instagram stories anonymously only when the story is publicly available. A safe viewer should not ask for your Instagram password or promise private-account access.
Safe flow
Copy the public username or profile link, open the viewer flow, then continue in Telegram when available stories are found.
What to avoid
Avoid password requests, one-time-code requests, browser extensions, APK installs, survey walls and pages that claim to unlock private stories.