An alternator, such as an automobile has, has a rotating field with two leads to it. Is this polarity sensitive? It's only a fancy electromagnet, I don't see where polarity matters. Am I right?
No it doesn't matter, the output is AC anyway, and is rectified to give DC.
It WOULD matter though in a dynamo, where the rectification is done mechanically (by the brushes/commutator).
In fact with a dynamo on an old car you can reverse it's polarity simply by reversing the car battery and pulsing the field coil, to make it's residual magnetism the other way round.
As Nigel says, it doesn't matter. It changes the phase of the AC waveform by 180 degrees with respect to the rotor pole positions but that has no effect on the rectified output.
Bear in mind that the rectifier diodes are probably inside the alternator, so what comes out from the alternator terminals is DC. Polarity then does matter.