I can see how the oldest three kids, having been undiagnosed Aspies for some time, might be able allow the parents to convince themselves that they just have "eccentric" kids. But when Sarah was born, that should've had the parents thinking, "Wait, what's going on here..."
MADDuck also suggested to me that they are probably Mormons since one of the kids' name is Nephi, which is a name in the Book of Mormon. I assume anything that hints at planned parenthood is something they'd find distasteful.
I think it's an interesting way for viewers to understand that autism is a spectrum. Really, there's no easier way to show this than to have a family that falls on different aspects of the spectrum and to have that family have its own series. Awareness is a good thing, right? But I hope there'll be more truth than distortion as the series goes along...issues and circumstances can easily get mishandled by those behind the camera who may have an agenda or are ignorant.