Hey Moonfish,
If a patch interferes with one of the mods, causing the game to crash, than you should disable the mod to play the game. Now regarding continuing your campaign, it depends. Some mods change the game to a point where the saves become incompatible with the vanilla game. Other mods don't do that.
Most moders will make a note in the mod description (on the mod web page) if it breaks compatibility with the vanilla game. So if you are considering using a mod, read through it's description. If you're not sure: launch the game with the mod, start campaign, make a save, launch the game without the mod, load the moded save file, and play for a bit.
If you already have a mod and the game stopped working after the latest patch, go to the mod website and see if there was an update released, maybe your problem was already resolved. If not try launching the game without the mod and load the save file, if it works, it works.
All mods I've used so far - Detailed Character Customization, Fast Dialogue, TournamentXP(no longer using this one), and Bannerlord Tweaks - don't break the saves files.