The Portal for ArcGIS Map Viewer prompts for credentials after opening a web map which includes an item with stored credentials from a stand-alone server and the basemap contains a mixture of Portal for ArcGIS and ArcGIS Online services.
This issue is not reproducible in ArcGIS Enterprise 10.8.1, the current minimum supported version of ArcGIS Enterprise. If the issue occurs in newer versions of ArcGIS Enterprise, contact Esri Support Services.