

“How many divisions has the Supreme Court?”
Even of a judge deputized someone to arrest an executive branch officer, it’s unlikely to actually happen. It always ends in who has bigger guns and that’s going to be the FBI, the Marshalls, or the secret service. No deputy trying to arrest someone on a bench warrant is going to get into a confrontation with a fellow LEO protecting said arrestee.
My contention is that the DOJ (who oversees the marshals) would order them to ignore the bench warrant.
Courts have the power to deputize whomever they choose. If they were to deputize, for instance, a state police officer because the marshalls wouldn’t carry out their orders, my belief is that no deputized agent would arrest someone for contempt if some LEO under federal control (FBI, the marshalls, capitol police, etc.) was protecting the person held in contempt. You will not get two sets of cops shooting at each other over this.