Hi Larry!
12v+ ---> fuse ---> Instrument switch---> NMEA load ---> BatteryNeg
12v+ ---> fuse? ---> fuel solenoid button ---> fuel solenoid ---> BatteryNeg
So, how can the NMEA circuit fuse blow? I assume it is a quick blow type fuse, so transients are a possibility. Either 12v+ has to be higher or BatteryNeg has to be lower for the voltage and current across the NMEA load to increase.
Sounds like Raymarine tech is a good place to start. Is it possible that the SeaTalk fuse is providing the power for NMEA 0183 and especially the converter somehow? Maybe it needs a different power source.
The NMEA converter could possibly have some internal voltage regulation going on, even a DCtoDC converter. If it senses that 12v+ is, let's say, 9.5v+, then it might compensate by drawing more current at that lower voltage and that could blow the fuse. As Steve notes, the voltage thing is relative. The same result could happen if BatteryNeg is not 0v but +2.5v.
If your NMEA circuit is connected to a monster buss that doesn't wiggle a bit voltage wise and the ground side is equally stable, then maybe you'll have to look for more exotic causes. Coils such as your solenoid can produce spikes when the current flow is interrupted. Alternator systems when starting and stopping can do so too, as mentioned above.
I'd be curious what happens to the voltage reading across the NMEA load when you push the stop solenoid. It probably won't show on a voltmeter if it's just a transient spike.
I hope my thinking aloud might give you some ideas.
Sounds like the old troubleshooting question: "What changed?" is pointing to that new converter load.
Let us all know what you find out!