I have had this problem occasionally with rubber parts of camera gear, fortunately never with a camera body rubber.
But the other day I took out my Spyder screen calibrator that had been kept in a sealed container and the entire body of it was horrendously sticky. The body of it is primarily hard shiny black plastic.
Cleaning was done with a cloth and neat washing up liquid which did not address it completely and then 'hand sanitiser' and now seems good. First time I have seen plastic affected.
I would try Hunter Boot spray that conditions their rubber boots.
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