Religious beliefs are allowed in the Inner Sanctum as are world views, upbringings, etc... Outside the castle SCJ's are not prohibited from participating in the political sphere and of those who do I presume it doesn't come from a lack of input and thought. What defines impartiality?Never thought it was a state secret that the judicial oath contains a pledge of impartiality. But if you want to question an SC judge's veracity under oath, then I can't help you.
“I, _________, do solemnly swear (or affirm) that I will administer justice without respect to persons, and do equal right to the poor and to the rich, and that I will faithfully and impartially discharge and perform all the duties incumbent upon me as _________ under the Constitution and laws of the United States. So help me God.”