I've read in more than a few articles that some cruisers use hydrogen peroxide(3-5 %) in their tanks which would eliminate the chlorine taste. IIRC, 1/4 cup for every 100 gal. did the trick and would run the 'drinking' water thru a filter of choice. I do not recall if Mexico was part of the cruising area in the articles, but I came away from the articles with the impression the hyd. peroxide killed all but the nastiest particulates. Cheap and comes in it's own non-corrosive container!
As for drinking 'watermaker' water, I did that for 6 days on a trip. I was not familiar with the system, but wished we had one of those "Waterworld" gizmos for recycling...not too tasty!