Good question. I've seen some research on using a type of algae to produce an oil usable by diesel engines - but that's very different from avgas. So maybe-someday for the kerosene-burners (and, to be fair, modern 'high bypass' jet engines are basically a type of propeller married with an inner jet powerplant that also contributes thrust)

I didn't read these closely, but, as I remember, they were using CO2 from powerplants to get a higher rate of production from the algae - so it's not at all clear that this approach constitutes "carbon-neutral".