That photo of 'Raleigh Nylon Extra' tubulars is from a tire that's rotted away, and for display only, so there is no danger of me riding them (and even so, here in san diego we hardly have any rain.)
Here's a theory about why nylon tires might be WORSE in rain. First, vulcanized rubber is vulcanized rubber, whether it's vulcanized to a cotton or nylon casing. HOWEVER, a fully inflated tubular with a cotton casing may be more 'flexible' than a similar nylon casing tire, which, at its maximum pressure, might be totally inflexible, like a latex vs. butyl tube.
So rain lowers the coefficient of friction between the rubber and the road. However, the cotton tire is more supple and rides like a squished sponge, so has a large contact area with the road and good traction in the rain. A fully pumped nylon tire behaves like a rigid body, with very little surface area on the road, and when you lower the coefficient of friction for that small area, you pass some handling or steering minimum friction point and the bike becomes dangerous to ride?
- Don Gillies
San Diego, CA, USA