It seems like cats could certainly be an effective source of ESD. Not sure how much of an issue that would be with loose hair but certainly petting the cat while handling sensitive components during dry times of the year with being grounded could be a seriously bad idea.
I'm sure any sort of contaminant on a circuit can affect it. That could be by promoting corrosion, conductance, capacitance. Even if the contaminants themselves don't have problematic properties, they can absorb moisture from the air, which does.