The OP asks, “Could the issue of Passover have been one of the reasons they refused to execute Christ?” I believe the answer is yes, the timing of Jesus’ capture and execution during the week of the Passover festival did play a role in the decision to have Pilate execute Jesus.
Their original plan, as @Anne so deftly points out, was to wait until after the Passover to surreptitiously capture Jesus and kill him.
Matthew 26:3-5 ESV
3 Then the chief priests and the elders of the peoplegathered in the palace of the high priest, whose name wasCaiaphas, 4 and plotted together in order to arrestJesus by stealth and kill him. 5 But they said, “Notduring the feast, lest there be an uproar among the people.”
Those who sought Jesus’ death had planned to wait until after the feast, but at some point they changed their minds. The catalyst behind this change was likely the appearance of Judas with his offer (Mt 26:14-15). Based on the presence of the Roman soldiers at Jesus’ arrest, the new plan of action involved the Roman authorities from the outset.
John 18:3
So Judas, having procured a band of soldiers and some officers fromthe chief priests and the Pharisees, went there with lanterns andtorches and weapons.
If Pilate were the one to kill Jesus, Jesus’ opponents could bypass several obstacles that stood in their way. One was Jesus’ popularity among the people and the possibility of public backlash. Two was the problem of timing given the rules against hearing trials during the Sabbath or holidays (Ancient Jewish History: the Sanhedrin).
Trials were also supposed to be held only during the day. The issue of timing helps to explain why Jesus was brought before the religious leaders during the night and handed over to Pilate in the early morning.
Ellicott’s commentary on John 18:28
And it was early.—The Greek word occurs in the division of the nightin Mark 13:35 (“even,”“midnight,”“cock-crowing,”“morning”) for thetime between cock-crowing and sunrise, as we should say roughly, fromthree to six o’clock; but comp. Matthew 27:1, and Luke 22:66. We mustremember that Pilate must have sent the band (John 18:3), and wastherefore expecting its return.
By having Rome execute Jesus, they could sidestep the rules and procedures that regulated how the Sanhedrin conducted criminal trials, not only those that determine when trials could or could not be held but also those that protect the rights of the accused. When Jn 18:31 is examined with these motives in mind, their response to Pilate’s question is revealed to be a cleverly disguised confession.
Pilate must have known what they wanted, and surely they didn’t have to explain to him of all people the Roman constraints on their powers. In other words, their answer was a truthful admission that, if Jesus were fairly tried according to their laws, it would be unlawful of them to execute him. In fact, if they tried anyone else according to how they tried Jesus, it would not be lawful for them to execute anyone.
John 18:31
Pilate said to them, “Take him yourselves and judge him by your ownlaw.” The Jews said to him, “It is not lawful for us to put anyone todeath.”
By manipulating Pilate into doing their dirty work, those who sought Jesus’ death thought they could keep their hands clean. It was the same twisted logic that made them think themselves undefiled simply because they did not step into the praetorium (cf Mt 23:23-28). While they must have thought themselves very clever, based on Jesus’ words to Pilate in Jn 19:11, the only ones they were deluding were themselves.
John 19:11
Jesus answered him, “You would have no authority over me at all unlessit had been given you from above. Therefore he who delivered me overto you has the greater sin.”
