A good paint for kitchen cabinet doors?
Application quality is probably more important than a specific paint. MDF sucks up paint better than most wet and dry vacs. Sealing it well (especially any edges/routed elements) is absolutely key.
This is a good example of the issue and a possible solution
You would have to get MDF pretty soggy with paint for it to significantly warp the doors. A much more likely issue is gonna be the paint cracking as it shrinks rather than 1 mm of drying polyurethane paint warping a 20 mm MDF door.
If I'm being honest solid wood or birch plywood is probably easier to get a good looking result out of. That way you can go for paint, stain or naked and finish it off with some clear polyurethane for protection.