I had not given it much thought, but it occurs to me that I eat far more rye bread now than I did before I moved here. In fairness, the most popular form of rye bread here is not the type of bread that I associated with it when I was growing up. I always pictured rye bread as something close to pumpernickel, with caraway seeds in it. Winnipeg-style rye is actually very light, and baked in a manner that makes for good toast, but awkward sandwiches.
One poster in the forum suggested that sandwiches made with rye bread are popular here because folks wouldn't live in Winnipeg at all if they did not like a challenge. It's hard to argue with that.
The population here is anecdotally divided along cultural lines when it comes to their choice of rye bread as well, with the Jewish community favouring it from one bakery, and the Ukrainian community preferring it from another. There is a third major bakery in the background jumping and waving and calling, "hey, we make it too!" Other than the shape and size of the loaves, I cannot tell much difference between the bread produced by the three major players here, though I was not born here, so my opinion on the matter is tempered by being a recent arrival versus people born into the rye situation.
While Winnipeg rye is the predominant player in the market here, there are obviously other styles available as well. Many breakfast places will give you marble rye if you order rye toast in the morning, and some of the fancier restaurants will sneak dark rye into the complementary bread plates they serve before a meal. One long-established steak house has their own in-house dark rye with a salted crust that atara and I both really like.
On a broader note, Winnipeg has a few cuisines that - while not unique - are an integral part of the local dining experience. If I was going to list five foods that I consider integral to the Winnipeg culture, just off the top of my head I would list:
Honey Dill Sauce
As a fun footnote, if you happen to visit Winnipeg and want to get a group of people into an argument, ask them how to spell "Perogies" or "Koubasa".