actually the romans didnt have much to do with it. The roman judge thought he was innocent and could see through everyones hatred of him. Even the jewish king Herod found nothing wrong with him. The jewish religious leaders were the ones who hated him bc he was threatening their cultural dominance bc they were using the synagogue to manipulate the public and Jesus didnt appreciate that.
They just needed permission from pilate to execute him but pilate really did not want to and even after he obliged he immediately said "I wash my hands of this" and then he wrote "the king of the jews" on his cross.
The reason he even did that was because an anti-semite gained the trust of the roman emperor and tried to overthrow him and so at that moment anyone wanting to please the emperor would try to gain his approval by being good to the jews
The whole thing was political