Are they Christians? Or Quiverfull cultists?
Personally, I don't consider the quiverfull movement to be cultic. If folks want to have as many children as God sends them, I'm for it as long as they can support the kids.
The Duggars are part of the Bill Gothard cult. Gothard dictates the style of clothing (women covered neck to feet, like Islam), length of hair, etc. And Gothard himself had to step down over allegations of sexual abuse/harassment by 34 young women.