Going by your other examples, shouldn't it be Luddist and not Luddite? English is famously inconsistent and is a difficult language to learn, owing to it's linguistic heritage, as it's a bunch of exceptions to rules. Like i before e, except after c, but also in a bunch of other words, so every English student just needs to remember those.
Yeah, maybe not the best examples. There are other "-ite" words, but I can't recall off the top of my head any such that also have "-ism" forms. It is, as always with languages, "just the way it is": I've always seen it rendered as "Luddite", never "-ist". (Maybe because it's named for a person, not a thing or principle? Tried to hint at that possibility with his full name.)
Yup, English may be the most inconsistent of languages. When I was a kid, we used to blame French for being "just exceptions to rules, exceptions to exceptions, and exceptions to those exceptions!", but with a few decades of perspective... Nope, English is far worse.
