It has origin in 4chan, like a lot of memes, and is at least as insulting to its user as to its object - being in essence an insult directed at functional adults by caricatures of NEETs, the humor coming from the fact that the latter really aren't in a position to look down on the former.

Of course, as with any hot meme, it gets a semantic makeover in the course of widening adoption, but if you're looking for an answer to the question of whether someone who uses "normie" unironically, especially in a context outside Reddit or a *chan, merits taking seriously...well, at the very least, I think it's reasonable to interpret that at least as a strong clue that the user isn't in the habit of thoroughly considering his utterances before emitting them.