I would suggest extra bracing with Baltic Birch (BB). You should also consider laminating BB over mdf. Best of both worlds, so to speak. North Creek Music uses layered for one.
The thing is that they are not the same, and building the cabinet should keep that in mind. 13 ply BB is what I would recommend if you do decide to use just BB. I personally have never seen the real deal at my local Home Depot, try a real woodworkers store. It costs about 3x mdf. If you can find a 5'x5' 18mm (~3/4") sheet for around $65 you are doing good. If the stack of so called BB at the store is full of badly warped pieces that would be a clue that it might be something else.
"Baltic" birch grows slower because of the colder climate and is denser than other Birch. I would be careful selecting BB if you don't know much about it, there are a lot of grades, stuff being called Baltic Birch is not always what you think it is.
Some thoughts and info, hope it helps.