Well, from my perspective, if you have a babysitter that you like, your DD likes, and she is satisfactory in most ways I would not let a couple of Doritos and Spongebob be the hill to die on.
When I was a kid, my siblings and I loved the nights our babysitter came over. Yes, we watched more TV (or movies) and ate less healthy snacks, but we had a lot of fun and really, in the big picture, no harm was done and a lot of fun was had.
I can't see firing a sitter over this, but then, even though I wouldn't eat Doritos or sit through an entire episode of Sponge Bob myself, I do let my children enjoy both of these things on occasion. I mean, I get that these are things you strictly forbid, and it's your kid, but most teenagers (and even adults) don't see the harm in a few chips and not-so-fabulous cartoons from time to time.
If it were me, I would allow the kid to let loose a bit when the babysitter was coming over. Unless it were an every day thing, I know my kids would enjoy it. In fact, they go to daycare once a week every Sunday night while DH and I are in Love & Logic parenting classes and they love that there are movies they haven't seen and they get to have boxes of cracker jacks and capri suns for snack (the daycare provides these - I guess I could all out ban it, but it's once a week).
eta: I do understand that it would be extremely frustrating to have a sitter who didn't follow your rules - but the examples are pretty innocent, IMO, and not things that would be put your child in immediate harm. I would have some deal breakers myself, but an incident like that wouldn't be included.