Well, especially in regards to rule-following and existentialism Kant seems like a great touchstone. As I read him, though his purposes were clearly different from the existentialists, he kind of lays a foundation for existential thought. This is because freedom is such a central value to his ethics. In a way, if we take him at face value as saying that the categorical imperative says the very same thing in each iteration, his only criteria for whether a rule is moral is
1) Does it wind up contradicting itself if every moral actor follows it? If no then go to 2 --
2) Are you motivated strictly from a sense of respect for the moral law when you act on such and such a principle? If yes then moral, if no then at least legal but not moral.
which allows for a greater range of actions than a lot of moral systems before Kant.
Now where Nietzsche differs is probably on the emphasis on 1 -- the possibility for universality isn't as important to Nietzsche. But what Kant did is articulate a way of ethical thinking that allowed an individual to act on their own conscience in spite of whatever surroundings they may find themselves in -- so your society may believe that such and such is good, but as long as you believe otherwise and you are acting out of respect for the moral law and everyone could theoretically adopt your rule then your action is moral.
In other words he articulates a way for moral rules to be private
in a particular sense -- if not quite in the sense I take the private language argument to mean when it describes a private language.
What's really interesting about Kant's rules is that what makes them moral is
not the rule, though the rule must actually pass some formal criteria, but the
motivation behind an actor's act. So we can have several persons who are following the same rule, are acting in the same way, but only the person who knows in their heart of hearts that they are doing it out of respect would know that their action is moral (at least if they are Kantian, of course).
Hence why this all opens up thinking, or perhaps serves more as a propaedeutic, to existential ethics -- it's about one's relationship to a rule, and its motivation, and largely excludes our social milieu. Nietzsche just takes this line of thinking further, absent its reliance on theological underpinnings (which are pretty obvious whenever we read Kant, even if his formal theory does not rely upon theology).
So this gets back around to, in my mind, on just what we mean by private or public -- because a private rule by Kant is still, in principle,
articulatable (oi, I butcher the language so), even if it is not shared. And though it be articulatable we can have no
behavioristic criteria for determining if an act is moral, though we can check if it follows the rule.
(a few edits for clarity)