The page you linked is what I meant.
When you run the game from Windows, it uses the INI files stored in "C:\Users\[username]\Documents\My Games\Fallout 4" but when you run the game from Mod Organizer, it uses the INI files stored in either ModOrganizer\profiles or "C:\Users\[username]AppData\Local\ModOrganizer\Fallout 4" so you might check to see if the ini files used by Mod Organizer are different from the ones in My Games.
The only other thing I can think of is that certain game overlays (e.g. software that allows you to chat and stream while playing) have been known to cause the game to crash when using Mod Organizer.
I've never used the VR versions of the games so I don't really know how they're different from the standard versions of the games.