Will horizontally polarized antennas set in a "0 degree" versus "180 degrees" configuration always behave identically? Well, watch this video...
Same applies to vertically polarized antennas set to 90 degrees versus 270 degrees, and all the combinations in between with their 180-degree counterpart.
As mentioned earlier, these observations cannot be generalized, where the magnitude of the differences observed are specific to one's QTH and circumtances.
But the implications of this experiment are very consequential. That is, it is possible that for most EME antenna arrays that use fix polarity (H and/or V), the selection between 0 and 180 degrees for horizontal Polarization, and the selection between 90 and 270 degrees for vertical polarization may have a measurable impact where one configuration may yield lower noise compared to the other, translating directly into a performance advantage! This should be considered by the EME practioners when making that selection. The video above is a proof that this phenomenon is very real (1 dB difference in this case).
***WARNING: For Best Resolution, it is critical to select 720p HD resolution in the youtube "settings" at bottom right of the player. The 360p default setting won't yield good enough resolution to see the details. It will take several seconds before the High Resolution kicks in, so you will need to restart the video from the beginning when the High Resolution is active and select to view the video in "Full Screen Mode" for best experience...***