A friend advised me on this, so I'm posting it here right away so that someone else can get advice.
Try a fake reinstall, throw the entire The Sims 4 folder in Documents to the desktop, launch the game (it will create the folder again, completely empty) and see if it works -> create a new game/family and play. If it works, then there is an error in the files where you had mods, saves, etc. I would try to throw the save files (your saved games) there first and play to see if it does anything stupid. CC clothes, furniture, etc. will of course not be in the game and will be deleted, so don't save the game, just try to see if it works and then turn it off at some point but don't save the save.. (if you save it, you won't get the CC there anymore and you would have to put everything there and change it manually!)
So if it worked for you, then the mods are to blame, I would recommend cleaning them. For the most part, these errors are due to the mods, or to a lesser extent, just a corrupted save (if it didn't work without the mod). And then there are a handful of game errors, which in this case I don't think it will, because it works for everyone else.
This way you can deduce whether it is a game bug, a save bug or a mod bug. To sort it out, you have two options: • either you can try using the Better Exception mod, MCCC which throws LastException or maybe Mod Manager or other online tools. • 50/50 method = you throw half of the mods folder aside, start the game and see if it works (if so, the bug is in the half that is gone), if not, the bug is in the part that is left there, and keep sorting it out until you figure it out.