“Pale” isn’t an exact synonym for “white”, as in “white picket fence”, but it’s pretty close. And as everybody who’s grown up in or even visited suburban areas in the US, a “picket fence” is a pretty standard thing to have around the front yards there, and nearly all of them are painted white. But there’s an unexpected redundancy hidden in “white picket fence,” if you know where to look.
“Picket” showed up in English in the 1600s. It meant a pointed stick, and came from the Latin word “piccare” (to pierce) by way of the French “piquet”. The English “picket” was a stick (or “stake”, which is pretty much the same thing) that you’d put in the ground as a marker. Another use for a picket was to tether a horse, particularly if the horse belonged to a soldier — since soldiers would be likely to need to tether their horses out in the field instead of in town where you probably wouldn’t need a picket.
Using a picket to tether soldiers’ horses gave rise to a new meaning for “picket”; posting troops to watch for enemies came to be called “picketing,” “picket lines,” and “picket duty.” “Picket line” and “picketing,” as you know, are still in use, mostly for protests and organized labor strikes. Since in those situations many people carry signs attached to stakes, there’s a common belief that “picketing” has to do with the signs on sticks. But nope, it was the soldiers’ horses.
Another use for a “picket” was to hold up a fence. And therein lies the hidden redundancy I was talking about in “white picket fence”. An older name for a picket used to hold up a fence was a “pale” — derived from the Latin root that’s also behind the modern word “pole”. There’s another English word “pale,” meaning “lacking color.” This one is from the Latin word “pallidus.” So there’s a “pale” that’s a pole, which is a picket in a fence, and the fence is usually lacking color, so it’s pale, or white.
And there’s yet another meaning of “pale:” “beyond the pale” means outside normality or beyond expectations. This one comes from fences too; back in the day “beyond the pale” was simply “outside the fence.” Over a century or two the phrase gradually took on a metaphorical sense that now is its primary (probably only remaining) meaning. But at one time if you really were beyond the pale, the pale you were beyond was made of pales. Maybe pale ones.