It's weird, I don't understand them at all.
One of my best friend is a neocatechumenal due to family but he's different from all the others, he's pretty popular and has none of the cringy things the rest of that group usually does.
OP, you say they are cultish. From what he told me they are cultish indeed (even though he isn't personally cultish). They mostly marry among their group, they their own mass every sunday without mixing with diocesans, they do easter and christmas on their own at different times than the normal mass, etc…