Making cabinet doors for my island that I renovated.. Eventually I and going to replace all my kitchen cabinet doors and drawers. But for now I am starting with the island. I have 4 doors to make and the are going to be painted light gray when I'm done. I'm using popular for the rails and styles and mortise tenon joints.. I plan to route a 1/4" dado for the panel insert.

What should I use for the insert?
I was going to use 1/4 plywood but since it is going to be painted is there something else I should use so I'm not fighting the grain showing through the paint or have to use a grain filler.. I read people use mdf. But my fear is it absorbing moisture since its in the kitchen.

I would go ahead and use the 1/4" dado even though modern plywood is metric and about 7/32" thick. You can glue the panels in which will help the strength of the door. Then the gap left you can just caulk that before painting. You could use birch plywood. It paints well and is easily available.

Poplar and birch are woods that are tight grain so there is no need for a grain filler. That is better used on woods such as walnut and mahogany. Sometimes people grain fill oak however with oak it's generally acceptable to see the texture of the wood in the finish.

I would not use MDF in a kitchen. MDF is literally paper, the same kind of paper that grocery sacks are made out of. Being paper it reacts to being wet just like any other paper. It will swell up and disintegrate. MDF is a product better suited to make cabinets for commercial work like in stores where it is often covered with formica. In any case store fixtures are generally changed out every few years and really only considered for temporary use.

I don't like the 1/4" plywood. It makes the cabinet doors feel light and cheap.

I put a 1/4" rabbet on 1/2" plywood and flip it around so the back is flush with the stiles and rails. Makes for a sold cabinet door and the drawer pulls are through solid ply, not air.

I kinda like that idea..

That's exactly what I do, works very well. I use birch plywood and also use birch for the faceframes. Harder than poplar, more dent resistant. One other thing, lightly sand the plywood faces just to remove the fuzz, before assembly.
Mike Hawkins

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Can you take a picture of the backs?

What about joints. What do you do for the rails and styles... In the pics I can see the stiles have a tongue that goes in the rails. But does that interfere with the rabbit that you cut for the plywood back.

Here's the back and front of a prototype large drawer front I built.

I'm actually not going to use this method for my kitchen cabinets. I didn't like the mismatch between the maple veneer plywood and the maple hardwood. I'll be using glued up hardwood panels for those.

But I'll be building my master bedroom vanity like this since it's going to be painted.

The stile and rails are cut with the Freud 99-762 shaker panel set. You can probably get a cheaper shaker set if you're not going to need long tenons for doors with glass.

Hawk, it looks like your birch panels match pretty nicely. Does that stain up nicely?

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What I was planning to do is mortise tenon the rails and stiles. But will my 1/4 said interfere with my stile tenon

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Your 1/4" slot down the middle of the rail will go right down the middle of your mortise. I don't think that should be a problem.

I do t have a pic of the back, but they look like the pic Android posted. I used a dado set on my table saw to cut the grooves in the rails and styles, also made the tenons with it too. These doors were finished in white conversion varnish. When your cutting this many pieces, the dado set made quick and easy work out of it.
Mike Hawkins

So..... I guess if using my router to Cut the dado on the rail and styles for the 1/2 inch plywood panel I would use a 1/4 inch straight cut but and use the plywood to set up the fence.. Macking the bit flush with the end of the plywood? Is that how you would do it

You could do that, but I would do the rails and styles first, then take some plywood scraps and make some test cuts with the router and check the fit between the plywood and the groove in your rails and styles. Plywood is a bit undersized so you may not end up with your 1/4" bit flush with it. You don't want a sloppy fit, don't want it where you have to pound it in either.
Mike Hawkins