Should I apply polyurethane to the bar rail before or after the epoxy pour?

Apply the polyurethane before you pour the epoxy, and make sure it is oil-based polyurethane.

The bar rail itself should get lacquer or polyurethane rather than epoxy. UltraClear Bar & Table Top Epoxy self-levels on a flat surface; on the slope of a rail it won't level properly and you end up with waves or brush strokes. So finish the rail first, then pour the top.

If you're also using oil-based polyurethane on legs, feet or other parts that won't be coated with epoxy, keep in mind that it has a slight amber tone, the same as epoxy. It isn't noticeable unless it's over something completely white.

Oil-based polyurethane is also the sealer to use under the epoxy if the top was painted with an oil-based paint. Oil-based paints take a long time to fully dry, so apply 3 coats of oil-based polyurethane to seal the surface before the epoxy seal coat. Going straight over oil-based paint that isn't completely dry risks the epoxy not sticking and peeling off months later. Latex and water-based paints are the better choice under epoxy; the epoxy can go over them in about 24 hours.