I don't have any problem with wood causing rust. You need to use well dried wood. I like walnut because it's oily, or kiln dried Maple, and if I use 2x4s I make sure they are very old and dry in my shop. New 2x4s have water. I use a meter to check my wood.
And oil in the holes can not hurt.
And let me say that a lot of quality tools come in wood cases or holders