Jo Mano actually wrote a paper on coloring that she gave at the Association for American Geographers mid-Atlantic meeting last year. See pp. 24-25. In short, it's connected to older conventions that refer to the Biblical naming of the sea as red, and so it's a common convention from medieval T-O maps and other mappaemundi as well. Remember that most geographers producing these maps, and most of the people buying the prints, would never lay eyes on the Red Sea. Therefore they placed great stock on classical and Biblical accounts and the reflection of those things on the map, and such maps would presumably reflect a more learned (and thus reliable) cartographer if they included that convention which learned people expected to see. As you might imagine, this would be a bit confusing to those who did actually go visit the place, so it took time to die out even after Portuguese activity was commonplace in the area.

[edit: Obviously there are a lot of maps that are uncolored entirely, or missing this convention, so it wasn't universal--but it was a recognized part of a map as a text.]

Coattail question: I have a redletter Bible (in which all the actual words of Christ are in red) that contains maps in which all of the Biblically significant features are also colored -- Sea of Galilee, Bethlehem, the Red Sea. Is there a connection? Or is red just the other easily available ink?