All my bolt actions, lever actions and my single shot have wood.
My military rifle all have fiberglass, plastic or metal (except for my M-1 Garand and my 1931 Mosin Nagant)

I have used every one of them to kill game with except the Mosin.

That includes my AKs my ARs and they killed all the deer and antelope with one shot each, except one time with an AR in 6.8 SPC in which I made a 1st shot too far back on an antelope and made a 2nd shot to finish it off.

I have also killed a fare share of game with my Flintlock rifles and 7 animals with a long bow with wood arrows.(5 deer, one elk and one antelope) I have never missed with my muzzleloader or needed a 2nd shot, but I sure have with my bow. More than I'd care to admit.

So I am of the opinion that it is the hunter doing the work, not the tool in his hands. Use what you like.