1. There is an argument for the ten commandments as a judicial symbol -- as much as we can have a statue to the personification of Lady Justice without legislating Paganism. Justice Moore himself killed any chance of that, though, by declaring his intention to "honor God," which I think we agree runs afoul of the amendment.
2. The separation between church and state at the judiciary level is, at its heart, about a system of justice that does not judge a person by alien standards. Thus the Bible's denunciation of homosexuality falls short as a cause for sodomy laws -- but so does secular moral disapproval of it. But flip that around. What cause is there to enshrine "diversity" as a good other than simple "secular moral approval" of it -- a moral approval, in fact, that some on the Supreme Court literally took on faith from the University of Michigan? No, it seems to me that if "We think [sodomy] is bad" doesn't work then "We think [diversity] is good" (Michigan's actual argument) doesn't either.
3. I don't think it's possible to have impartial judges. Like you said, all of them have beliefs that influence their decisions. But the left pretends otherwise, as we see with judges like Bork and, lately, Pryor -- whom Russ Feingold implied was too bigoted to serve on the court because he changed the dates of his family trip to Disneyworld so it wouldn't coincide with Disney's "Gay Day." See, a right-wing judge who believes a law is unjust (e.g., abortion) is outside the mainstream, not to be trusted, in danger of legilating from the bench, etc. Never mind that many of the liberal ideas we hold dear were at one time dissents against "settled law" (Dred Scott, Plessy). That's why I characterize modern liberalism as, effectively, a religion.