I've only been able to reproduce this on UWP so far.
Steps:
- Sign in to the app
- Load one of the user's web maps
- Zoom to a location where data for that web map appears
- Select a new basemap to display
Based on some testing, it appears step 3 is essential to getting the odd behavior. If I preserve the map extent to an area where the web map does not show data/layers, changing basemaps seems to work fine.
Screenshot on UWP:

I've only been able to reproduce this on UWP so far.
Steps:
Based on some testing, it appears step 3 is essential to getting the odd behavior. If I preserve the map extent to an area where the web map does not show data/layers, changing basemaps seems to work fine.
Screenshot on UWP:
