Personally I think you ought to stick with beer... that's part of the ritual that dates back to times when times were tough! It's basically peasant food, so why waste a good bottle of wine?
But if you must drink wine. You can certainly drink ether Red or white wine.
For the white I would ideally suggest a Gewurztraminer from Alsace, or perhaps an unwooded Chenin Blanc from South Africa (my favorite would be the Raats Original).
For the red wine I would suggest an Oregon Pinot Noir (drouhin makes nice ones!), a Zinfandel (The dry creek valley area in Sonoma California is among my favorite areas), or something in the grenache family that could included southern France, Spain and a couple from California. The Pinot is ideal if you want to compliment the meal, and you could go with a nice burgundy, but that would be quite wasteful along side such an unworthy counterpart. A Garnacha from Spain is perhaps the politically correct wine since it is very inexpensive and perhaps in the "peasant category", and it does represent a very good pairing scenario... I might even enjoy the corned beef with a good garnacha! The zin would be my choice in most cases in an effort to mask out the entire meal. Zins with their lively fruit and high alcohol would clean the palate even after the foulest of cabbage!