I have a story map that is shared publicly. I double and triple checked all of the maps within it and all of the layers are also shared publicly. I checked our organization page and it allows anonymous viewers. I'm also mostly certain that it didn't require a sign in a month ago and I didn't think we changed anything, but I do know there were a bunch of ESRI updates since we last made edits.
Here is the link to the storymap: https://storymaps.arcgis.com/stories/059861db45fe45fc88c9f3aa0ff7aabb
...all connected to the same VPN, which might have a filter or blocker that is causing the login prompt. If so, try accessing the story while disconnected from VPN....
As @Anonymous User suggests, it's time to give your IT team a call. I have a love/hate relationship with VPNs: I love to hate them...