Each side of the airplane has a set of sensors. The ones on the left (while sitting on the plate) are named Captain <sensor_name> and the ones on the right are named First-Officer (F/O) <sensor_name>. The MCAS software would switch from Captain AoA vane to F/O AoA vane between flights. The location where the pilots are sitting doesn’t affect how the airplane is flying itself. The person flying the plane can be sitting on either of the two seats, but the most senior pilot usually sits on the left.
It's not that the MCAS software would switch. It's that the sensors feed into two different flight control computers (Captain and F/O). And which FCC is primary would switch after each flight. Both FCCs run the same software, but with different inputs from the different sensors.
