I have mixed feelings too. I've seen the show once and the family does seem happy. And they can afford to have them, so...
But on the other hand, as others have said, it's hard to believe they can give 19 children, especially 19 children that close in age, the love and attention they need.
I understand wanting to have a large family, I'd like one myself. To me that means 6 or 8 kids, though! However, just for me personally, I feel that having that many biological children would be sort of irresponsible, so I plan to adopt in addition to my biological kids. But anyway, where was I going with this? Sorry, it's two in the morning here.
The religion thing kinda skeeves me out too. I'm a fairly religious person, but, wow. And no, most American religious families I know don't spank their kids!
So...rambling here, but YABU in that it isn't totally your business, although as someone pointed out, their going on TV sort of makes it our business. But YANBU in that, yeah, 19?! C'mon!