No, you cannot at any time reverse the polarity of the voltage across polarized capacitors of any kind. They will explode. Therefore you cannot use electrolytics and tantalums in situations where the signal is bipolar.
What are you trying to do? If it's just bypassing, use ceramics- they are not polarized but have the potential to distort signals if you use them for something other than bypassing unless you are aware of a few things.
You can operate a tantalum or electrolytic capacitor in reverse but you have to limit the current. One way to make a non-polarized cap is to connect two polarized caps back to back in series. The capacitance is 1/2 the capacitance of each one if they are equal. If the voltage is millivolts, you can use a polarized cap just as if it were non-polar.
There's normally no need to use a non-polarised capacitor (and it would be disadvantageous to do so), as there will be a polarising voltage across it - but you need to ensure it's the correct way round!.
Accidentally blow up a tantalum cap, breath in the vapors and you'll find yourself waking up in a hospital minus some brain cells .... if you're lucky!