Clippy can care about rationality in itself, or it can care about rationality as a means to clipping, but it has to care about rationality to be optimal.

Well, if you want to put it that way, maybe it does no harm. The crucial thing is just that optimizing for rationality as an instrumental value with respect to terminal goal X just is optimizing for X.

I mean "not subjectivity". Not thinking something is true just because you do or or want to believe it. Basing beliefs on evidence. What did you mean?

I don't have to mean anything by it, I don't use the words "subjectivity" or "objectivity". But if basing beliefs on evidence is what you mean by being objective, everybody here will of course agree that it's important to be objective.

So your central claim translates to "In view of the evidence available to Clippy, there is nothing special about Clippy or clips". That's just plain false. Clippy is special because it is it (the mind doing the evaluation of the evidence), and all other entities are not it. More importantly, clips are special because it desires that there be plenty of them while it doesn't care about anything else.

Clippy's caring about clips does not mean that it wants clips to be special, or wants to believe that they are special. Its caring about clips is a brute fact. It also doesn't mind caring about clips; in fact, it wants to care about clips. So even if you deny that Clippy is special because it is at the center of its own first-person perspective, the question of specialness is actually completely irrelevant.

In what way?

By being very incomprehensible... I may well be mistaken about that, but I got the impression that even contemporary academic philosophers largely think that the argument from the Groundwork just doesn't make sense.