We have a custom light gray basemap that is shared to everyone. When I create a map in Arcgis.com the basemap is an option to use. However, when I open a map in a groups gallery map viewer, I do not have the option to access my custom basemaps (i.e. Switch Basemap) even when I am logged in with my AGO account. How can I make my custom basemaps available as an option within the Application Templates and Group Gallery map viewers?
No, there is no way to do this in a hosted manner. You could download the application, modify the code, and host it on your own web server. This would require some coding.
I know that the Basic Template references the group that contains basemaps. You can edit the index.html file and change the group to your group with custom basemaps. (Note that your basemaps groups consists of web maps. Only the basemap inside the web map will be the actual custom basemap. Layers on top of the basemap won't display as part of the custom basemap.)
Thanks,
Mike