The Birch ply offers one more option for finish than mdf you could always just stain the birch you cant just open up a can of minwax and hit your mdf
You can, but it looks like crap that way. Actually, if the joints are perfect, with no glue or fasteners showing, it doesn't look
that bad, in an industrial way.
MDF needs to be well sealed to keep the paint from soaking into the edges more than the smooth surfaces. Since most cabinets built by weekend warriors will have some divots, nail/screw holes and little/not so little gaps, Bondo is about the best filler to use. Lay it on thin, sand it smooth and repeat, as necessary, to get the smoothest cabinet possible. A filling primer should follow, with more leveling and dust removal. Once it's as smooth as possible, any kind of paint can follow. I just painted one with Krylon Indoor/Outdoor Satin Black. I wasn't going for perfection and I did it with the garage door open, which sucked since the wind kicked up just as I finished the second coat. If I feel like it, I may sand it again and go for perfect but it's only a test box and when I get to the point that I need to paint a lot more at one time, it won't be from a can.
More and more often, new and remodeled homes are being trimmed with MDF molding and casework because it is so smooth and stable. Other than the dust and glue being an irritant, it's very easy to work, but at 105#/sheet, it's best to have a helper if full sheets are moved.