I think "Norm" recently dealt with this problem by going thicker,
and then thinning the edges so it fits in a 1/4" slot. Perhaps
it was the 2nd fireplace episode.

Best of both worlds: Sturdy, and no slop at the cost of a little
extra work.

Tom H wrote:
I am making two mission style rail & stile doors (21" x 75")
I had planned on using 1/4" oak plywood for the panels (2 in each door)

1/4" (3/16" actual) oak plywood seems kind of flimsy.
Would I be better off using 3/8" (5/16" actual)