How to make dish drainer board from plywood shelf
Several coats of polyurethane would work. Acrylic likewise. Epoxy would work. Per @DMoore's comment on some other question, redguard would do, but would stink for several weeks (as might the epoxy, depending on epoxy formulation.)

Be sure to coat both top and bottom and especially edges. Top and bottom to reduce warpage that you'd be prone to if you only coat one side, and edges since plywood likes to fall apart if moisture gets in between the layers.

You could also possibly build this from "solid surface countertop" material - 1/2" thick plastic, pretty much.