I can certainly see the reason to use different fix for film and paper since (for me at least) they are different in terms of dilution. I have never given stop bath a second thought and use the same for film and paper. Pollution of the stop by the paper developer should be a non issue, since the function of the stop is to kill the developer in the first place. Anyway, I've never had any trouble using the same bath for both film and paper over the past few decades. When it goes bad, it lets me know.
Dean