I think it depends on the oil/fat. I think the word “rancid” conjures up the idea that it would taste like pure garbage, but that isn’t really the case. What you are tasting is oxidation (and technically some other reactions, too), and not all flavors of oxidation are “bad” flavors. Sherry, for example, is partly defined by the oxidation.
Most “refined” oils (e.g., soybean, peanut, canola) are going to be fairly resistant to oxidation because they don’t have many compounds that oxidize easily. Something like extra virgin olive oil or flaxseed oil, though, has a lot of compounds that can oxidize. That’s why some oils come in opaque containers, and warn you to keep them away from heat. Some, you even need to refrigerate. If you did side by side testing, you’d probably pick it up. Oxidation is one of the reasons you get rid of old fry oil; the heat speeds up the reactions.
Whole wheat, I can definitely detect the difference, and I’ve definitely had rancid avocado oil before. Nuts, I’m not sure about, but I think the flavor of an oxidized nut wouldn’t really be bad, just not as good.
The taste of oxidation is often described as “wet cardboard”, which I agree with for a lot of things. “Fishy” is another word I’ve seen for oil that’s gone rancid