is the code in question which it looks like should be:
midi.write((byte)0x00);
bitClear(leds,2); /* turn on green led */
bitSet(leds, 1); /* turn off red led */
updateShiftRegister();
(the only change being on swapped for off in the comments). While it is true that in code usually (but not always) 1 is true or on and 0 is false or off, hardware is different. If your leds were common anode (which I think was initially the case and is likely still the case) then 1 is off (as both sides of the diode are at 5V and it isn't lit) and 0 is on (the bottom of the resistor is 0V the anode of the led is 5V, current flows and light occurs). When you switch to common cathode leds the opposite will be true, the cathode connects to ground and when the shift register pin is 0 no current flows and the led is off, when the sr pin is high there is 5V on one end of the resistor and thus voltage and current through the led and the led is on. The software doesn't actually care which is which, making it the easy place to make the change as you would have to change led types from common anode to common cathode in the hardware to make this change, and only a 1 to a 0 in a text file to do it in software. If you are indeed still using the red leds, it may be profitable to change to the common cathode ones as they are what you will eventually use (although as noted the change is only a 1 to a 0 in the software).
Peter