Florida laws are pretty specific about car seats and booster chairs. Not only that, but nearly every city and county (including theirs) has car seat installation centers and services at at least one police or fire station in the city and/or county. There's also a robust free car seat program in Florida, and local to them.
They're not simple or ignorant, as they have seen children in carseats and parents strapping their kids in. They obviously needed one, or were sheepish about not using one, to take their baby home from the birthing center.
I agree that they probably figured nurie's lap was good enough, but I also think that in these fringe groups, there's a pervasive mentality that rules don't apply to them. It doesn't stem from religion so much as it stems from the fringe-ness. However, I can think of multiple examples where it does stem from religion. Whether they think they're blessed, or meant to die when they die,