Before everyone jumps on me let me state here and now that I am referring to a different locale/destination with my comments but I felt compelled to let folks know that there are some venues where the "it doesn't matter what side" does not apply.
I just returned from a 16-day cruise on HAL Rotterdam from Valparaiso to Rio de Janiero. We had a Deluxe Veranda Suite on the PORT side for the very reason that during the inland passage thru the Chilean fjords, the glaciers we would be seeing would in fact be passing on the PORT side of the ship. We were able to sit on our veranda with a drink and enjoy the the views.
The only glacier we encountered in a "cul-de-sac" was the Amalia glacier. We sailed in, hung out for a while, turned around and sailed out. We walked out on the fantail for that one to get "official" ship's photographer pics of us with the glacier in the background.
So, when rounding Cape Horn, if you sail from Valparaiso then you want to be on the Port side - if you sail from Rio (or BA) then you want to be on the Starboard side.
Again, I apologise for posting this on the "Alaska" site.