Seems crazy at first, but think of it this way: What if, after All Grown Up was cancelled, Chuckie had a nervous breakdown after being publically humiliated, then developed a bad coping mechanism, leading Chaz and Kira to worry? Then they send him to therapy, and he gets an eight month long spanking for his bad behavior, and then becomes Ned Flanders?
There are a lot of reasons supporting this: First, even though Ned is more religious and says "diddily dum doodily" a lot, his personality is still surprisingly similar to Chuckie's. They're both pushovers, both put up with verbal abuse from people they interact with often (Angelica and Homer). And they are considered "nerds" or "'outcasts" simply because they are less cool or different than their peers. Plus, I know they don't look alike, but sometimes, as you get older, your appearance can change (sometimes dramatically). And for Chuckie, I think he starts to look like Ned more and more as he gets older. Take All Grown Up for example. He starts wearing button up shirts like Ned. Eventually, he'll wear a pink button up and a green sweater. And his head shape will become more round like Ned's. He will also cut his hair short, dye it brown, and when he gets older, he'll grow a moustache. There's just one problem: Ned's moustache is red like Chaz's. Since he doesn't want to look like his dad anymore and wants his moustache to match his hair, he dyes it brown, too.
But how did it all begin? Why would he change his name? Why would he abandon his friends and family? Well, a lot of the Rugrats parents read a parenting book called Lipchitz, and since Ned is religious, he thinks books like that are evil. The reason being the dramatic alter in life? In a late 1996 episode of The Simpsons called "Hurricane Neddy", Ned has a nervous breakdown after his house is destroyed in a hurricane and verbally abuses everyone in town. Then he think's he's lost it and goes to therapy (again). In therapy, you find out a lot about Ned's childhood. First, his parents don't like discipline (I believe it has something to do with Lipchitz again), so Ned dubs them as "No good beatniks". Plus, Ned's parents bear a striking resemblance to Chaz and Kira. Creepily so. When he is finally cured, he doesn't want anything to do with being a Finster or his friends and family anymore, so he runs off to Springfield, becomes religious and assumes the identity of Ned Flanders. There are still a lot of questions regarding this: If Chuckie is Ned how does he turn yellow? Why do they still call him Ned when he was a kid? Well, the Rugrats universe is different than the Simpsons one. For example, almost all the Simpsons characters are yellow, whereas the Rugrats characters are not, so by default, he would turn yellow. And I think they still call him Ned because they don't want you to discover that he is Chuckie, thus subtly separating the two universes.