I have the exact same issue after today's update, and I managed to find out exactly why it's happening.
The game's keybinding system is currently broken and only works correctly if the Windows mouse settings are set to the default, right-handed mode.
If I turn OFF the mouse button swap in Windows, I can successfully bind the physical Right Click to "Fire" and the physical Left Click to "Aim", and the gameplay works fine. However, doing this completely ruins my Windows desktop experience and the in-game menus, because everything becomes right-handed, which is terrible for a left-handed user.
If the Windows button swap is turned ON (my normal setup), the keybinding menu glitches out and registers every single press as a "Left Click", making it impossible to bind anything.
DICE, your update completely broke how the game reads Windows-swapped mouse inputs. It worked perfectly before today. Please fix this input handling conflict for left-handed players!