@ErinReilly1 -- I asked several of my colleagues to check and we are all not getting prompted to log in. We're all on different home networks as well.
The only other thing I can think of is that maybe you and your colleagues who are experiencing this issue are 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.
If that's not the issue, the next step would be to please contact Esri Support as they can work with you to try to isolate what the specific issue might be.
Owen Evans
Lead Product Engineer | StoryMaps