Can I make cabinet doors out of mdf?
You shouldn't have any problems using MDF.

A lot of modern cabinets are made out of MDF these days as it's a cheap material to use. It comes in a variety of thicknesses so you'll be able to get one that meets your requirements.

You need to wear a mask when cutting and sanding it as the dust is not very nice.

It takes paint well and you should have no problem gluing strips to the face to give it some depth and character.