When I enter CAS in-game, there's a chance that the UI will just break, and I won't be able to click on anything. I can't exit CAS, I can't change my sim's appearance, I can't open any menus, so I have to close the game using task manager.

This has happened to me twice now. Once when I tried to give a sim a stylist career makeover, and once when I tried to give a sim a tattoo. It's not consistent at all, it doesn't happen every time I try to enter CAS from in-game or even just with the Ambitions features.

I don't have any UI mods, and none of my other mods should be doing this? Also, while I do own every pack, at the moment I only have World Adventures, Ambitions, High End Loft, and Fast Lane installed.

EDIT: after further testing it seems to be happening specifically when I try to use the ambitions features, like makeovers and tattoos, on sims in my current household. Whenever the error happens I get a "script error" popup from nraas errortrap, but it doesn't tell me anything more useful than that. I have deleted my cache files and it still happens, so that doesn't have anything to do with it.

Take the script error to NRass, it would be in your sims 3 folder in the documents folder.