First, the spacecraft is I believe fully automated. While there is the ability to pilot the craft manually using onboard controls, my understanding is that is already considered a backup or unusual scenario.
As far as the touchscreens themselves, my understanding is there are four touchscreens total, and each can represent / control every aspect of the vehicle. So if a single touchscreen fails, the other 3 provide redundant access to necessary controls.
Finally, the dragon capsule does have manual (non-touchscreen) joystick controls for the critical flight controls.
So these systems have enough redundancy that a touchscreen failure should absolutely not jeopardize the flight.