A judge's job is to apply the law without fear or favor, and stripping the party label off probate-judge races fits the biblical standard that justice should not respect persons — the question on the bench is what the law and the facts require, not which team the judge plays for. Supporters across the aisle, including the state's chief justice and two former governors of both parties, make the same case. The honest counter-argument, which a careful voter should hold, is that party labels give voters a quick shorthand about a candidate's judicial philosophy, and removing them can leave low-information down-ballot races even harder to judge. On balance this leans toward 'yes' for anyone who wants courts seen as impartial; just know that nonpartisan does not mean apolitical, and you will have to do more homework on the candidates themselves.
"Ye shall do no unrighteousness in judgment: thou shalt not respect the person of the poor, nor honour the person of the mighty: but in righteousness shalt thou judge thy neighbour."
— Leviticus 19:15 (KJV)