I always wonder when this question comes up, which seems to be about once a month.
I make treen ware for fun, and always use EVOO to finish the spatulas, spoons, cutting boards, stirrers, tasters and beaters I make. I use just about any wood besides red oak, or some of the more tubular looking pieces of white.
Yet... in the last two decades I have never had any of the EVOO oiled kitchen ware go rancid, stink, rot, or pass disease to anyone that uses them. Cooking is my second hobby, and I use all of my pieces frequently, as do many I have given them to as gifts.
I stir fry in vegetable oil, pan fry chicken breasts in vegetable oils, and a mulititude of other tasks that expose my treenware to natural, non or slow curing oils. And while the spatulas and turners absorb vegetable oils and animal fats, no disease or pestilence to report. I cut bloody meats (15 - 18 lb pork loins into chops, raw chickens, and raw fish) on my cutting boards frequently with no problems. I beat/stir concotions with raw eggs and vegetable oils in them with my wooden beaters and haven't had foul odor one. This nonsense has been going on for years, and EVERYTHING has been treated with plain EVOO.
I know that many of us have their own favorite finishes, but I think that those that are afraid of vegetable finshes should use stainless utensils. So do any of the people here realize that for many years it was animal fats that were used to cure these utensils? Sometimes nothing at all? I have a great maple cutting board that I have had for years that I have never put a drop of finish on, and it is great. It has picked up some oils somewhere though as you can see the difference in the appearance of the wood on the front and back of the board. So that means it has picked up animal fats and oils from food prep. Yet... no smell.
A GOOD FIELD TEST: Take a piece of scrap from your project and treat it with vegetable oil of some sort. Wipe off the excess oil. See how long it takes to "go rancid". Your grandkid's grandkids will be shaving by the that happens.
I am going with Mr. Pawlowski on this one.... just put something on it! You'll be fine!
Robert