Failure to respect a proper dependency order can in the best case simply cause the game to crash.
This is potentially destructive for existing save files, as mod dependencies require that some mods be loaded first. As if it wasn't bad enough that Bethesda will place extra (and likely unneeded) files on your computer without prompting you or asking permission, reports have been surfacing that your load order (which facilitates the order in which mods get loaded first) is now forced to load your mods in alphabetical order.