Why are 120-volt multiwire branch circuits and 240 volt outlets not allowed on the inverter output of a stand-alone solar PV system? I understand directly off the solar panel at the DC combiner box only 120 volt exist, but on the output of inverter/charger I have found PV systems to provide 240 volts.
What makes you think that they are not allowed?
Some stand alone inverters only have a single 120V output. That means that you cannot run 240V loads.
And with only one polarity, the neutral current cancellation that makes MWBCs attractive does not exist.
If you have an inverter with 120/240 output, in the form of opposite polarity L1 and L2 terminals and a neutral, I do not see any particular reason not to run an MWBC off its output. Although if it is a Modified Square Wave (I don't like the term Modified Sine Wave) inverter there might be harmonic issues that affect the neutral current.
If you have an inverter with 120/240 output you may still benefit from a 120/240 V autotransformer to balance the inverter power to the two segments of your loads. If you have only a 120v output a transformer will be necessary for 240V loads.