I saw a great recipe for Beef Wellington on Serious Eats that I'm eager to try. However, my roommate does not eat mushrooms (both because he dislikes the flavor and because he had a bad experience as a child, so "hidden mushrooms" are out too). I worry that omitting them would defeat most of the purpose of the dish. Is there anything that could be used in their place to give a similar flavor?
I don't think you can make a Beef Wellington without the obligatory mushrooms, it essentially becomes something else.
The whole concept behind beef wellington is to keep the meat juices in by being surrounded by pastry but there's no reason why you shouldn't omit the mushrooms for something else. I really can't think of any other food substance that would replicate the flavour of mushrooms without being mushrooms other than truffle.
I would try something like a pork/onion sausage meat stuffing and being the time of year it is, perhaps with chestnuts as a possible alternative, either surrounding the beef or inside it.
I don't like mushrooms much either, I've made wellingtons with pate mostly, although I've experimented with chopped up brussel sprouts with some success as well. One thing I would like to try is yellow lentils but haven't had the opportunity.
You could still try mushrooms though if it's the texture your roommate doesn't like rather than the flavor. If it is texture then try making a rough paste out of mushroom and shallots rather than chopped up pieces. Or try shitakes instead.