What kind of temperament best serves a justice of the Supreme Court - and lower courts? There's an important difference between between being an originalist/activist justice and being a conservative/liberal (or whatever synonym you want to use). The former are descriptions of Constitutional philosophy, the later are political opinions or views. Judges are to have neutral temperaments. They are not to substitute their personal political opinions for the judgment of the electorate expressed through legitimate democratic processes when the law is not un-Constitutional. Some laws may not be wise, but that doesn't necessarily mean they are un-Constitutional. We don't need activist judges who too often don't respect the democratic process - whether they are politically conservative or liberal. Neither personal opinion should be expressed in judicial findings.
What we need are judges who are temperamentally originalist, who base their findings on the principles expressed in the Constitution, and who respect the judgment of the people. Originalists might be politically conservative or liberal, but because of their temperament their personal opinions are irrelevant. That's why it's inappropriate to inquire about their views ahead of time. And with originalists it doesn't matter, because what matters is interpreting the principles of the Constitution.
I'll say one other thing about judicial temperament. We need judges with a humble and accurate assessment of their role in government. The judiciary is a third equal branch of government, with its own important role. But because justices are appointed rather than elected, we leave much of the checks and balance of this branch to their own temperament. So we need to know they recognize their role as interpreting the Constitution, rather than substituting their own judgment for other democratic processes.