I think the comments about storage are spot-on. Disposable diapers aren't really made with long shelf-lives in mind, and what may appear to be a sealed bag will, over years, let the outside environment in. I've experimented with vintage (20+ years old) Pampers and Huggies diapers when the eBay prices were right (which is rare), and I've run into several bags of "stale" diapers. The most common symptom has been that the padding, which usually expands considerably once the diapers are removed from the bag, has instead become permanently flattened. As well, I've run into non-sticky tapes, non-stretchy elastics, and significantly diminished perfumes. Following several big disappointments, I finally concluded that buying vintage disposables with the intent to use them was just a bad idea.
But I certainly wouldn't worry about exceeding the "use by" date by a few years, and certainly not for safety reasons.