Since the release of Anniversary Edition, I renamed my Skyrim SE installation folder from 'Skyrim Special Edition' to 'Skyrim Special Edition Classic' before updating the game on Steam. If anyone needs any further details on this, or would like to see it in action, I can record and upload a video walking through this. Unfortunately if you reload Fallout 4, all your mods in the Mods/Load Order will be unselected, meaning you have to re-enable all your mods once again, and at this point, I'm fairly certain every time you load up Fallout 4, because atleast for me it's not saving which mods are active. I think as long as they as they are checked on the left-side panel the game will detect them. In Mod Organizer on the right-side panel in the Plugins Tab, all your plugins will be unselected, but this doesn't particularly matter, as Fallout 4 still detects the mods installed through Mod Organizer. If you're lucky, you might be able to load your save, otherwise you'll Crash to Desktop. After enabling mods, the game will have to reload the data files.

Unfortunately, Fallout 4 is looking here to find out what mods are active, so you need to go into the Load Order (hit T on the keyboard), and Manually enable all your mods. This leads to Bethesda's new mod portal which people can upload mods to which console users can now utilize. In the Main Fallout 4 menu, there is a new 'Mods' entry.

Solutions have included adding * at the start of esp files in the 'plugins.txt' in the 'appdata/local/Fallout' folder, but because Mod Organizer (atleast for me possibly because it had been read-only) hasn't touched this file, this obviously doesn't work.

Fallout 4 mods not working after update