Does a common neutral between solar inverter and utility affect current measurement?
You don't mention where you are. However, in North America, the Incoming Neutral conductor is bonded to Earth ground.

The incoming phase conductors pass through the utility power meter. This meter measures both incoming voltage and the current on each phase. These measurements are used to calculate the amount of power consumed by your premises. 

In other words, the amount of current in any Neutral conductor will not influence the utility power meter. 

Your electrician may be thinking of the problems that will occur if one tries to share a Neutral conductor after a GFCI device. If the current on that Neutral conductor is not exactly the same as on the phase conductor coming out of that GFCI, the GFCI will trip. 

You should still check both the relevant electrical codes and the manufacturer documentation to ensure that you are not inadvertently introducing a potential problem. 

Provided you don't exceed the current rating of the Neutral conductor, you should be okay.