switch OpAmp down to minimize power consumption
Opamps with shutdown pins do exist, but they tend to be on more specialised ones, since the standard dual and quad opamp pinouts don't have room for shutdown pins. It'd be worth looking to see if there are any that satisfy your requirements, however, as there are some very good low power opamps out there that will also draw less current when active than your current solution.

Using a P MOSFET between the battery and the rail splitter is also a valid option. Bear in mind that P MOSFETs have higher on resistance than their more common N MOSFET cousins, though given the power draw you're likely dealing with that's probably not a problem. Make sure the FET you select has a suitable gate voltage; if your MCU is running with the split rail as gnd, you've only got 3 volts to work with.