Create a specific "scene" tab within the ArcGIS Online and Portal settings in order to define a basemap gallery and default basemap for the webscenes - different from the basemap gallery and the default basemap for the webmaps.
Currently, only "map" settings are available (within the "map" tab) and apply to the map viewer AND the scene viewer. But global scene mode is only working with WGS84 and local scene mode requires a specific tiling scheme. Consequently, if the default basemap is not based on WGS84 and doesn't use the supported tiling scheme, an error occures opening the scene viewer and the basemap is dropped.
This idea has been marked as a duplicate to The way AGOL manages basemaps for 3D scenes