No, I cant, but then again I shouldnt have to. You are the one who should have to prove the bias. Does removing the tablets somehow make him any less/more bias. His beliefs havent changed whether they are there or not. Does the physical presence of the commandments somehow cause him to be less/more biased depending on his proximity to them?
Then you would have to apply that to every judge. If he were a jew would he have to prove he wasnt biased against non-jews? Has he been shown to be biased in other rulings he has made?
Applying this same logic, only non-religious people would be eligible to be judges, but then would he/she have to prove they have no bias against religious people?
Then, because he is white, does he now have to prove he is not biased against blacks, or orientals.
Because he is male, would he have to prove to you he has no bias towards females?
Where does it end? I dont think you are calling this judges impartiality into question simply because he ia a christian, but it sure sounds like you are.
Suppose he wants to wear a crucifix on a chain around his neck? What if it accidentally hangs outside his robe one day in court? Is he all of the sudden biased because of this outward show of his faith? Should he be not allowed to wear it at all? The crucifix and the tablets represent basically the same thing. If the physical presence of the commandments somehow affects the judges ability to be fair and impartial, then it is the judge who is at fault, not the tablets.

Werent we talking about a school at some point?