Can Radial Electrolytic capacitors blow up from AC?
Electrolytic caps are polarized, they can indeed blow up if you get polarization wrong or apply a higher than rated voltage to them. Same goes for tantalum capacitors, these can be even more dangerous.

If you look at the capacitor, there is a + and a - sign on it, they're there for a reason.

Depending on what you are trying to accomplish, a series diode or a diode bridge may be a solution, but it is hard to tell without a full circuit diagram of your set up.