When clicking your "completed projects" link I can see the sign in displays. I'm also running the web logging tools at the same time, and I see a flood of web requests. I note a couple item Ids display in the log. I'm able to use Item Syntax "https://www.arcgis.com/home/item.html?id=" with the ID number, and found this following Subscriber Layer was called on.
https://www.arcgis.com/home/item.html?id=986e0b86c8e447549aaecbed728538f0
When this item opens as a map, you will be prompted to sign in as this requires an ArcGIS online account to access.
A simple fix is removing the layer from the public maps, but here is blog that covers the use of layers like this in public facing content.
Use Living Atlas subscriber content in public maps and apps
I hope this helps.
-Adam