Hansel and Gretel's reincarnations all have blond hair and blue eyes, and if I remember correctly Ney is an Irregular. But wait, actually, wasn't her yellow hair explained to be because of her father being lucifenian (and not because he was a mud golem?), her eyes were yellow, despite being an irregular. (Part 1 because it won't fit)
Arte, Pollo, & Lemy however, have yellow hair and blue eyes, so were they also reborn irregular way or is it because they were irregular? And if the latter was the case then why does the same thing not apply for Ney? Could this be a mistake on Mothy’s part?
I’ll admit to being a little confused by what, exactly, you’re asking, but I will try to explain the situation as mothy seems to have set it up to the best of my ability (which is a tad difficult because he’s left a lot of it vague).
First off, having blue eyes is not a requirement of being irregular at all. This is a misconception that got spread in the fandom because most of the Irregulars are Kagamine characters (unless I’m an idiot and misremembering something, but pretty sure I’m not). Gallerian only states that they have golden hair. So Ney having yellow eyes has no bearing on whether or not she’s an Irregular. Her having golden hair is a result of being an Irregular (though it may be a retcon–it is possible mothy originally envisioned Arth as human, and that Ney having blonde hair was just a result of her genes, but in any case that’s just a red herring with current plot developments).
Second, Hansel and Gretel’s various incarnations all look like them as a result of some unspecified “fate” as per their reincarnation (that they are fated to be born as the same people each time). The implication we get is that the reason why Ney looks different from them is because Allen and Riliane were originally intended to be the reincarnated bodies of Hansel and Gretel. Abyss leading Prim to “seduce” Arth resulted in Gretel being reincarnated first, and because it wasn’t in the intended twin bodies she was born alone with a different appearance.
As for whether or not Arte, Pollo, and Lemy were born in an Irregular way–there’s no information on that. We don’t know how Arte and Pollo were born, and we don’t know the circumstances that led to Lemy’s mother getting pregnant.