As long as 125% of inverter output current falls between 500 and 540 amps then this falls under the 'next size up rule' 240.4(B). Note it's the same for the 300mcm CU on the line side of the disconnect. There's no standard size between 500 and 600A.
As far as the neutral, it's highly unlikely that the neutral current from the inverters is more than a tiny fraction of the phase conductor current. And see 220.61(A). Most likely the neutral is still oversized. That said, it would be legit to ask for documentation supporting the max loading of the neutral if they haven't provided that. And it doesn't make much sense that they didn't also spec a smaller neutral on the line side of the disconnect.
There's also 705.28(C)(2)*, but they don't seem to be invoking that because the neutral is larger than the EGC. Also perhaps that 15A breaker at bottom is a monitoring load that uses the neutral.
*2020 NEC citation, formerly 705.95(B).
