Did They Run Out Of Walnut!
 

Or another reason?

It's easier, cheaper and faster to mold bakelite or plastic, than to carve, checker and fit a piece of wood. And P-38 grips are somewhat fragile around the curved back edge if they are made out of wood.

What Doug says...

They definitely tended to run out of walnut during the frenzy of wartime production, evidenced by beech-wood grips of late WWI. The guys who checkered wooden grips at the factory could certainly fly! I saw a film clip from a link once posted here, of a Mauser tech doing it. He seemed to be using a 5-line (or more) cutter and zoomed across the grip! Scraps from making K98 stocks provided much of the material, IIRC.

I have heard that Mauser used Walnut and Beech “leftover” pieces from rifle stocks as the primary source of wood for Luger grips. By1941, most rifles were being stocked with laminate material. Hence less wood for grips.

The P38 pistols primarily had plastic grips from day one. They used wood filler (sawdust) later in the war to stretch the plastic resin.