Do high and low side labels on bidirectional logic level converters matter?
Yes, they matter. See that body diode on the MOSFET? It must be reverse-biased when both signal lines are being pulled high.

Otherwise, the HV side is trying to pull the LV side higher than the LV supply voltage. If that wasn't a problem, you wouldn't need the level shifter in the first place.



If you can find a MOSFET that doesn't have its substrate internally shorted to the source pin (i.e., it is brought out to a fourth pin), then you can do what you want. Connect the substrate to ground (the most negative point in your circuit), and then you can use the source and drain terminals interchangeably.