Well. Unless you actually want to kick Kate out of the family (in which case...Damian and Jason have to go too), I think readers need to be okay with what she did, or at least okay enough that they don't leave.
Perhaps because I don't believe in the "no kill rule", at least when it comes to self defense, I'm not as bothered here, because many of the objections to Bruce's policy raised are my own - but I also think that Bruce is not shown to be wrong in not wanting to kill. Tim definitely agrees with him, and Dick leans heavily in that way. Even Babs doesn't make an argument against the no-kill rule, she just says that as an adult, Bruce has to treat Kate as another adult.