They're by far the best fast food place around (faint praise maybe, but still true). They have waffle fries and the best lemonade around, so the fact anything else tastes good is just icing on that cake.
The thing is that they're an exceedingly Southern company. They're on courtesy and hospitality, but they're also big on traditionalism. In my hometown, they're far from the only company who close on Sunday or take on extra staff for purely customer service roles (the biggest grocery store chain in town didn't even sell alcohol until a year or two ago when they were bought out by a national chain). The only difference is that Chick Fila is the only one that is so overt in their traditional Christian side. They come from a strong tradition of family-based, Christian businesses and they reflect a large part of the South's customer base, but in expanding to the size that they are now, they will get more press and more customers that don't agree with their beliefs.