Any kind of oil will go into solution when you put it into hot wort. Mineral oil would be food safe, but it could cause problems of with head retention in your beer. Any kind of film forming finish (urethanes, epoxies, etc.) will eventually fail, and chips of it could end up in your wort. Before that there would probably be harmful compounds leached out by the hot acidic wort.
Best bet is to leave it unfinished. I made mine of cherry, and only finished the handle portion (that doesn't contact the wort).
I've found that it's important to thoroughly spray it off as soon as possible after brewing, before the wort has a chance to dry on it. I still wash it with the other stuff, but the spray off makes cleaning much easier.