There are few definitive statements on what may damage nylon. With regard to maintaining harnesses the NZ harness manufacturer Aspiring Enterprises on it’s website sez

“Chemical damage is rare, as nylon and polyester are immune to most common chemicals, including detergents, lubricants, paints, solvents, and fuels. Spilling petrol on a harness will have absolutely no effect on it. However, nylon is attacked by acids of moderate strength, and polyester by alkalies, so sources of these, such as lead acid batteries and alkaline cleaners, must be identified, and care must be taken to isolate them from webbing equipment.”

They also warn against bleach based detergents.

Who knows this might even be true. There may be some published work on chemical damage of climbing gear. Needs a litterature search.

I avoid putting a rope near a washing machine and would wash one in a basin with clean water only. Possibly the suggestion for sewing machine oil is good if it’s a very clean light oil. Ropes should never be stored anywhere near cleaning agents or acids. The fumes alone can be enought to damage the rope.