It was the Romans who actually killed Christ. The Jews weren’t allowed to at the time.
The Jews turned Christ over to the Romans for the purpose of execution. They practically begged Pilate to crucify him. The Temple was corrupt and they corrupted their people. Pilate represents moral relativism; “what is truth?” he asked. Pilate was afraid to stand up to the Jews and say no, even though he knew Christ was innocent. Jesus, his mother, and most of his followers were Jewish. I think the point of the POTC was that it was our sins that crucified Christ. Everytime we sin, it’s another lash, another blow, another nail. Try not to sin.