Apparently the usual practice for Roman crucifixion was to strip the person to be executed naked. They wanted the punishment to be humiliating as well as extremely painful. But it’s possible that they made an exception in Judaea because of Jewish sensibilities—I don’t know if there is specific evidence for how crucifixions were carried out in Judaea.
Supposedly, Jewish authorities sometimes used nakedness as punishment. When temple guards fell asleep on duty, they were liable to be being beaten, stripped, and sent home naked as punishment.