Last night I dreamt that I downloaded a mod for Fallout 4 which adds a romance-able companion called Rachel. The catch was that the marriage to the spouse in the intro was baked into my save, and I had to start a new game with the mod installed. Otherwise, she would only say that she doesn't date married people.

Which got me thinking - I know this sort of problem was present in Skyrim, so how likely is it going to remain in Fallout 4? Will uninstalling mods be possible without disastrous consequences?

Depends on the changes they made to scripting. Most of Skyrim's problems were because scripts got baked into saves, so a savegame would start throwing errors when it referenced a script that no longer exists in the game. Generally harmless errors, but they can add up, and the really bad ones will bloat your save up like it got Corprus and FEV at the same time.

Now, something like what you dreamt about would be an artistic decision by the mod author. The only Skyrim mod I can think of that demanded we start a new game for it to function properly was the Civil War Overhaul; but that's because that mod is just so massive and script-heavy, and civil war quest data is ingrained into almost the entire game.

I hated this about some mods and once I figured out what was happening, I got more cautious about which mods I used. Some mods apparently used ~hidden perks~ to grant effects to items or characters or, as noted above, scripts that would lie dormant and if you removed the mod then those hidden perks and scripts would try to "call" mods that do not exist any more, and throw your game. I finally figured out how to re-install the mod, then perform a "safe" extraction, using console commands to stop scripts or remove hidden perks, etc. and THEN un-install the mods.... but of course Console players won't have a "console" to use for commands (I believe, which is ironic given the name).

Changing vanilla records may require a new game. For instance, I made Maven non-essential and attack the player if they choose a certain choice but it only works correctly on a new game.

Which is why I'm more reluctant to try mods for Skyrim. Granted, my modded Skyrim works better than my modded Oblivion.