Almost all biological waxes melt at temperatures close to 60C. The beeswax cannot leach out into food any more than the oil does.
I buy and eat comb honey. I like both the taste and the texture. The bees do not like to work the little wooden boxes. So as a premium commodity, the price goes up. Memories of my childhood, far away.
Here's the process. These are physical facts, not opinion.
Preheat the kitchen oven to 170C/340F or so. No hotter necessary.
On a mesh cake rack over a sheet pan, slather the wooden utensils, dishes, etc with oil or melted beeswax.
Into the oven for 3 minutes and 30 seconds by the clock. We aren't making chips.
OK. Out of the oven to cool, take a look:
Charles' Law predicts that heated air expands. Fact.
You see that as strings of little bubbles of wood air in the liquid oil/wax.
Charles' Law predicts that cooling air will contract. Fact.
So as the wood cools, the remaining wood air contracts and sucks the oil/wax down into the wood. Brush with more oil if you feel like it.
That's done for keeps. Boiling soup is approx 100C. That isn't hot enough to move the oil in the wood. Hot dish water can't move the oil finish.
As a note added in proof, many old wooden spoons are blackened from heating and sucking in food juices as they cool. Those decompose like the bottom of a compost box. It's just a physics trick you can take advantage of.
Here's an old pic of the production.