I wouldn't use MDF for doors. Not very robust and very hard to make paint look good on it.
Consider using plywood, and glue a strip of matching wood on the edges so you can cut the shaker profile on it. This would be for a solid door. If you are making a paneled door, you are basically makng a solid wood frame, and using thin ply for the panels.
The ply and solid wood edges will take almost any finish you want to apply. Stain, oil, wax paint, it won't be a problem. Just don't over sand the ply.
Splurge and go for some Baltic Birch ply. You'll love it.
Make certain you table saw blade is exactly 90 to the table or you'll have trouble gluing on the solid wood trim to the ply. Apply a pre coat of glue to the plywood edge, then glue again to help make the trim stick. Use lots of clamps and cauls to hold the trim firmly in place while the glue dries.
Use a trim bit to make the trim the same thickness as the ply. Work face down so the front trim and ply edges align.
The more I do, the less I accomplish.
Last edited by DesertRatTom; 03-14-2019 at 02:29 PM.