Over time, any petroleum based lubricant will erode wood. I do not know about the synthetic lubricants but I would suspect they will do the same thing. The cellulose fibers in the wood become soft when saturated with oil. It is best to store guns with the barrel down so the oil will not drain into the wood. A light coat of sealer finish is also a good thing over the often unfinished internal areas of a stock.
However, if you use a Precision Fit Stock as I do, you have little worry.
Pat Ireland