Why was Jesus nailed to the cross in a diaper?
I don't mind answering questions, but as (presumably) we are both adults let's not be silly. You are asking if Jesus was naked on the cross.
Part of the humiliation of the Roman crucifixion is that people were indeed hung naked on the cross. Back in the day of Jewish executions, Jewish males were stripped naked before they were stoned, so it is doubtful that Jews would have asked or even have been given special consideration to wear a loin cloth when the Romans took over capital punishment.
It was common practice that men were stripped before being handed their cross (the crossbeam) and were whipped naked until they reached the place of execution.
Scriptures tell us that Jesus was not stripped until they reached the place of execution (possibly because Jerusalem was swarming from people coming into the city to celebrate Passover). While most artists later added a loin cloth for sake of modesty, Michelangelo was a notable exception.
Modesty sort of comes and goes. At one point there was naked statuary in Vatican City, but fairly early on, someone had the bright idea of adding fig leaves to the original art.