The polarization of the electromagnetic wave has a strong influence on the resulting antenna pattern. But to consider polarization in the resulting pattern, also the input patterns of the single antennas must have information about the polarization. But this polarization data is not available for most patterns of commercially available antennas.

So, if the input does not include the polarization, it makes no sense to consider polarization in the result. Therefore, the result is independent of the polarization of the signals.