We have (true) custom kitchen and our white cabinets have a light natural wood interior. At our cottage, which was also a custom kitchen, the dark cabinets have a similar light wood interior..

^^Exactly. In particular this idea that people have that the word "custom" is better. Sometimes yes it is. But what we see mostly on this forum is that "custom" from a GC's "guy" means old-style cabinets like they did in the 80s, perhaps with clunky partial overlay construction, and maybe one narrow stack of base drawers rather than base drawers throughout. If the cabinets are painted, a quality manufacturer will have a catalyzed conversion varnish baked-on factory finish, but a custom cabinet maker does not have that ability, and you may end up with chipping and peeling after a couple years.

My cabinets were made by the Amish. One thing I did NOT want was that plasticky looking whatever they put on cabinets you see at places like Lowe’s. They might as well be made of plastic. You can’t even tell it is wood anymore. I would take a few chips over plastic looking cabinets. Not sure though how this applies to painted cabinets. I wanted stained cabinets that did not look like they had a plastic coating.

"If the cabinets are painted, a quality manufacturer will have a catalyzed conversion varnish baked-on factory finish, but a custom cabinet maker does not have that ability, and you may end up with chipping and peeling after a couple years."

There is no advantage to baking on a cabinet finish. I would be surprised to learn any manufacturer is really baking on a finish, and if they are doing so it is likely likely just to save money and not to improve quality.

If a factory has robotic paint application it will be superior, however, there is no other real advantage to a factory sprayed finish. They are going to use the same basic products optimized for cost rather than quality and call it custom.

“'Real wood' is about the worst possible thing to make painted cabinets from. "

I suspect that the cabinet maker is just noting that he uses veneer cores rather than osb or mdf cores in his cabinets. Veneer core plywood is real wood oriented in different directions to stabilize movement. It is generally looked on favorably compared to engineered wood cores. I doubt very seriously your cabinet maker is joining boards for cabinets.

Nobody is using solid wood to build cabinet boxes. Hes talking about pre-finished maple or birch (less money) plywood interiors. Natural meaning unstained just clear coat.

Also nobody is baking a finish on. Cabinet part are put under heat lamps to accelerate drying so next set of parts coming behind them can be racked. The only baked finish is powder coating on metal where parts a sprayed with powdered paint with a static charge so it sticks then baked in ovens where that powder melts into a hard paint-like coating.

What matters the most is how good his painted finish on white shaker door. Technique, materials, equipment etc.