You do get non polar electrolytic caps, but not with as wide a range as the regular. If you have doubts about the input signal you could use one of those.
Or as a reasonable compromise look at the film foil plastic caps: non polar, non piezo but with higher ESR as compared to the ceramics.
The piezo effect may have made some people allergic to ceramics. In fact the cheaper hi-K ceramic caps if used as supply decaps can cause more problems than solving.