The gap between the drawer fronts on mine are 1/8". So this must be purely up to the cabinetmaker. Behind the drawer fronts, the space between the drawer openings themselves is closer to 1/2". Mine were made by a cabinetmaker in Dover, Ohio.

Find a better cabinet maker.

They told me a 1/4" gap is necessary to compensate for expansion and contraction of the wood. Also that the blade used to cut the veneer that'll be grain matched is that wide. I know there are no real standards but a 1/4" seems so large to achieve the below look, right? What should I ask for?

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At least these people are being honest. What they are really telling you is, sorry, we can't do what you want. Listen to them.

The gap on my cabinets is 1/8". Find another cabinet maker.