So, I took the cable to the Apple Store a few weeks ago. The guy at the Genius Bar smelled it and immediately replaced it with one that did not have the smell. He said he had not heard of other complaints about this (though clearly it is happening to others).
Then my wife got a new MacBook Pro (different model and charger - mine is the 15" with the 87w charger and hers is the 13" with the 61w charger) and right out of the box her USB-C charging cable smells like mildew/mold too! She's going to take it to the Apple Store before the end of the week to exchange it.
This is really ridiculous. Kind of amazing that this happened to us twice over a couple of months. As a previous poster said, this is clearly a supply chain quality problem that Apple needs to address. I'm surprised that I haven't seen this issue talked about anywhere else on the web. Given the fact that it's happened to me twice, those of us on this thread can't possibly be the only ones experiencing this.