Whatever the shooting board is made from, the blade of your plane should not cut into it beyond the first time when you "season" it. After you use it the first time, the plane will ride against a ridge at the bottom of the slot and your plane blade will only cut the wood you're trimming. So there's absolutely nothing wrong with making a shooting board out of MDF or plywood or anything else.
Solid wood does move so I favor some kind of man made product, but our ancestors used solid wood and it worked fine for them.
Go into the world and do well. But more importantly, go into the world and do good.