I don’t think Jesus blasphemed God, but others did.
You are correct that things were not legitamate with the trial of Jesus, and I can’t say exactly how things played out. If we take the gospel at face value, we know that they were divided over what to do about Jesus prior to that night and that some of them believed in him. We also know that the high priest Caiaphas and others planned to have Jesus killed (John 11:47-53). We see this sort of thing in our own politics between majorities and minorities. In order to keep things out of the public eye, or to take advantage of members not being there, things getting rammed through during midnight sessions of Congress. What is the difference?
And which of Jesus’ rabble rousing deeds got the attention of Rome? (he was a devout Jew who was faithfull to the Law after all).
Obviously some of his own people had to hand him over to Rome, and accuse him of political revolt (which put him in the same category as Barabbas). The high priest happended to be one of them. He threatened Pilate politically so that he would condemn Jesus to death (John 19:12,15,21).
Does that mean Pilate or Judas is off the hook? No! The complexity of the whole thing is obvious in the gospel account, and the personal sin of the participants is know only to God. We Catholics believe that Jesus was handed over according to the definite plan of God and “all sinners” are the authors of Christ’s Passion (because he died for all of our sins).