hello every one,
tecnically there is no problem shutting down both engines together, but there are some other considerations:
on b737, i always shut down rh engine first for 2 reasons:
1] for safety reason when parking at the gate & waiting for a gpu plug in. sop for my airline specify no apu if a gate+gpu is avail after landing.
2] if apu was started but not put on busses, to avoid putting every one(momentarily) & litterally in the dark at night.