This just in: you’re a knuckle-dragging, mouth-breathing moron if you say nucular and mean nuclear. But you probably already knew that.
People with a Southern drawl just can’t help it. We just have a hard time with words that have an L after a hard consonant. Like the word clash: if you listen to a southerner say it, it’ll have a subtle uh after the C to produce “cuhlash.” It’s fast (which is a weird thing in Southern pronunciation – usually vowels are elongated, emphasised, and embellished) but it’s there. Same thing with play (puhlay), flout (fuhlowt), and glad (guhlad).
But nuclear is a particularly hard word for Southerners. Not only do we have to deal with that tough “hard consonant followed by an L” thing, we also have to deal with a preceeding oo and a following ee.
This tends to morph what is usually an uh between the hard consonant and L into a eu or you. Thus nuclear becomes nuke-you-ler or nook-you-ler, depending on which part of the South you call home. (I tend to say nuke-you-ler, the same as Jimmy Carter, another Georgian, who is actually a nuclear engineer.)
It’s a regional thing. And since it’s confined to mostly the southern region of the US, I can’t help but think that the mockery of it is more of the usual snobbery from the Intellectual Elite. But then, if you pronounce nuclear nucular, you probably already knew that, too.