Wax Cotton Raingear
Keeping dry is tough without PVC, which tends to break down after a few years, and is hard to patch without the right adhesive kit.
Waxed Cotton is good stuff and a lower-tech solution.
As far as I can track it, it was developed by the British Navy for at sea use as a replacement for 'oilskins' (cotton or linen saturated in linseed oils).
While not perfectly water-proof, good fabric, well-designed and made keeps one substantially dry. The big pluses that it's very tough, repairable and the treatment is renewable. Any suitable design of cotton jacket can be treated in the field, so we can make our own. Other fabrics may work also (see comment below).
Treatments are mixtures of oil (most work, some are better... linseed was traditional but goes rancid... citrus oil blend may help?; mustelids (mink, marten, weasel, etc) are great but potent smelling); avoid used crankcase oil (carcinogenic)) and beeswax or equivalent (toilet bases are mounted on 'johny rings' of synthetic wax that'll do... dismount toilet from floor to scavenge).
The oil is primarily a thinner for the wax. You want a blend that is thin and penetrating when warm and cools to a paste or just crazing finish.
Some blend a little kerosene or gasoline (petrol) into the treatment to temporarily thin the mix and help penetrate fibers before evaporating off. For full effect, simmer fabric in the slew... but this can be dangerous. Consider cooking over hot rocks from a distant fire, and using a double boiler.
Cotton has the advantage that it swells when wet, so waxed cotton tends to absorb damp, then lock wet out. Thicker and higher denier (thread count) fabrics help. A lofty underlayer (such as a wool sweater) helps us stay warm against that damp. Look for this quality in synthetic fabrics if experimenting beyond cotton.
There are many good commercial brands with press-waxed fabrics (top o' the line). Barbour is a reliable brand, for one. Vacuum bagging or an improvised (hot) roller press (maybe even a wringer?) might improve DIY wax jobs, either of which might be possible in post-cataclysm years.
Dave Z