Vinyl seems to emit a gas which will react with and destroy many
substances. A good example is those vinyl book covers which have
turned the outside of many a book into eternal sticky mush.

It's not a gas, it's the plasticizer that keeps the vinyl flexible. I had the
same trouble with textbooks that had a kind "plastic-coated-board" covers. And
I've seen the plasticizer in patch cords attack plastic surfaces.

I am no aware of any plasticizer in the rubbery contacts of remote controls.

I've taken apart the keypad for my Ford. There is a silicone goo in it, which
I assume is there to prevent rust or corrosion.