Bill Everett's first Sub-Mariner story was first published in black-and-white—in the undistributed Motion Picture Funnies Weekly #1, in 1939—but it was colored for Marvel Comics #1 a few months later. On the first page, we meet Namor. He's underwater, which gives his skin a blue tint.
Here he is with his mother, Princess Fen. High-quality scans of this (very valuable) comic are difficult to find, but you can see here that they're both underwater, and both the same color blue.
In a flashback, we see Princess Fen in her younger days. Above water, her skin is white.
When Namor and his cousin Dorma emerge from the sea, they too are notably azure-free.
Here's Namor in Marvel Mystery Comics #3, with Betty Dean, a New York City policewoman. For whatever reason, her skin doesn't appear blue beneath the surface, but above water their skin is the same color.
Skipping ahead: here's the Atlantean Emperor Tha-Korr, Namor's grandfather, in Marvel Mystery Comics #7. Why, yes, he does look like a fish. Meanwhile, for the first time, Namor's skin is shown as white even when underwater. At this point, Everett establishes that Namor has a different color skin than most Atlanteans.
But the whiteness is catching! In Marvel Mystery Comics #10, both Namor and his cousin Dorma (who now has some creepy Walter Keane-like eyes) are below the water, untouched by blue:
Let's check back in with the family. In Marvel Mystery Comics #12, Princess Fen is still white, but now she's got Dorma's weird eyes, too.
In Marvel Mystery Comics #24, Namor rescues Princess Fen from a prison, but apparently doesn't notice that her skin is now green for the first time.
Marvel Mystery Comics #82, 1947. Namora comes to live with Betty Dean. Everybody's totally Caucasian.
Sub-Mariner #33. Phew! Even Fen is white again. Also... hmm. She's a redhead?
With Sub-Mariner #36, Namora's forsaken her own blonde hair for brown.
And that's how things were left when Marvel discontinued the adventures of the Sub-Mariner for the remainder of the 1950s. He resurfaced in the pages of Fantastic Four in 1961, and two years after that, in Fantastic Four Annual #1, the people of Atlantis returned, now as interpreted by Jack Kirby.
Remember Dorma, Namor's cousin? Well, now she's blue, for good. And—oh, family ties!—she and Namor are in love.
As of 1965's Tales to Astonish #96, Princess Fen is blue, too.
Sub-Mariner #1, 1968: in a flashback to the events of Marvel Comics #1, we see Princess Fen brought onto the American boat. This time, retroactive continuity requires that her skin be blue, to remain consistent with what Kirby had established.
....And the rewriting of history is complete: Invaders #20 reprints Marvel Comics #1, but this time, Namor and Fen have different-colored skin.
And that's pretty much how it's been ever since.