I've been searching for about an hour trying to find something that conclusively settles the question of whether wood is a good material for a wort-stirring spoon for the boil. I have come to the conclusion that there is much more religion than science accessible on this topic via a google search. I can't really find anything scientifically conclusive about it.
There are many sites whose authors claim that wooden utensils are prone to harboring bacteria. This seems to be a widely-held belief about wooden utensils, expressed on both cooking and brewing sites. Then there are a number of sources that claim that wood is naturally anti-bacterial. Some sites claim that wooden cooking utensils, tested a couple of days after having been used, cleaned, and air-dried, have been found to have far less bacteria on the surface than similarly used and cleaned plastic and metal utensils. None of the sources cited scientific references to back up their claims, one way or the other, so you just have to take it as religion.
I am not sure you can trust the boil to sterilize a wooden spoon. In fact, boiling doesn't sterilize; it only disinfects. But disinfecting is good enough for cooking or brewing. It takes five minutes of continuous immersion at boiling point to disinfect a utensil. No one is likely to do that with a wooden utensil due to risk of excessive liquid absorption and damage to the utensil. Nor would one likely leave it soaking in a bucket of Iodophor between uses, as I do with my SS stirrer. I'm sure there's no harm in using a wooden utensil to stir the wort while it is boiling, but I would not use it after the boil, just in case it were not adequately disinfected. It just doesn't make sense to take that risk.