The trick to this is to only download and install mods that don't use script extenders or replace files entirely. There are still quite a few mods out there that will work with Game Pass though. The Xbox app prevents players from editing certain file types, which means that several popular script extenders and visual mods will not work correctly with this version of Fallout 4.
Unlike modding a game that was bought on Steam or GOG, using a game through Game Pass means that it comes with certain restrictions. Before players just jump right in and start trying to install every mod they see they will want to keep in mind that this process isn't as simple as it may look on the surface level.