The first overarching issue is to determine what we mean by "responsible." How can one group say that the Jews are responsible for Christ's death and the other group says that the Jews are not responsible. The difference is precisely a lack of continuity in terminology.
What we must first consider is the philosophical notion that has been part of Catholic theology for over 1,000 years - the four causes. Aristotle was the first philosopher to identify all four kinds of causes which Aquinas would later incorporate in his Summa. Each cause is a different kind of answer to the question "why?
So, assume I am holding up a picture of the statue of David for you to admire. I ask the question, "Why is this a statue?" To answer this question, Aristotle can give four different answers: (1) This is a statue because it is made of marble; (2) because it is in the shape of David; (3) because Michelangelo sculpted it; (4) because Michelangelo wanted to depict the figure of David in marble (because he needed the money, perhaps). An account of each kind of cause is important for a full and accurate account of whatever a person is explaining.
Now let us return to the question, "Are the Jews responsible for the death of our Lord?" Let's rephrase that to "Are the Jews a cause of the death of Christ?"
Let's first consider the material cause of Christ's death. The material cause of a thing is the matter - physical matter - causing it to be. For our Divine Lord's death, it was the nails and the Cross which caused His ultimate Death.
Yet, what of the final cause of Christ's death? The final cause is the end (i.e. telos) for which something is done. We know from Sacred Scripture that our Divine Redeemer willing gave up His life on the Cross for the salvation of mankind. In this sense, many people will rightfully say that all sinners - thus all mankind aside from the Redeemer Himself and the Blessed Virgin Mary - are the cause of our Lord's death. After all, since our Lord died in order to save us, we are the cause of Christ's death.
This is where many people who say that the Jews are not to be held responsible stop in their argument. But, let us go further and consider the efficient cause of Christ's death. The efficient cause of a thing is “the source of the primary principle of change or stability,” e.g., the man who gives advice, the father (of the child) (source). For our Divine Lord, it was the cruelty and infidelity of the Jewish people that forced Pilate to condemn Him to die. It was their hardness of heart that brought about our Lord's death and they were the agents who beat our Lord, drove the nails into His hands, and ultimately crucified Him.
Thus, it is correct to say that the Jews are responsible for the death of Christ - if one means that they are the efficient cause of Christ's death. Let us be specific in our discussions - especially about matters involving philosophy since precise language is so necessary to understand a situation completely. And let us not shy away from the truth - while not politically "correct" - that the Jews in one sense are to be held responsible.
Let us conclude with a segment of His Excellency Bishop Williamson's Eleison Comments for this week on this very topic:
Firstly, the killing of Jesus was truly “deicide”, i.e. the killing of God, because Jesus was the one of the three divine Persons who in addition to his divine nature had taken a human nature. What was killed on the Cross ? Only the human nature. But who was killed on the Cross in his human nature ? None other than the second divine Person, i.e. God. So God was killed, deicide was committed.
Secondly, Jesus died on the Cross to save all of us sinful human beings from our sins, and in this sense all men were and are the purpose of his death. But only the Jews (leaders and people) were the prime agents of the deicide because it is obvious from the Gospels that the Gentile most involved, Pontius Pilate, would never have condemned Jesus to death had not the Jewish leaders roused the Jewish people to clamour for his crucifixion (Mt. XXVII, 20). Certainly the learned leaders were more guilty than the unlearned people, says St Thomas Aquinas (Summa III, 47, 5), but they all cried together for Jesus’ blood to come down upon them and their children (Mt. XXVII, 25).
Thirdly, at least Pope Leo XIII considered there to be a real solidarity between the Jews clamouring then for Jesus to be killed and the collectivity of Jews of modern times. Did he not in his Act of Consecration of the Human Race to the Sacred Heart of Jesus have the entire Church, from the end of the 19th century onwards, pray to God that he turn his “eyes of mercy towards the children of that race, once God’s chosen people: of old they called down upon themselves the Blood of the Saviour; may it now descend upon them a laver (i.e. washing) of redemption and life” ?
But Leo XIII is by no means alone in observing such a continuity amongst Jews down the centuries. Do they themselves not lay claim today to the land of Palestine on the grounds that it is theirs by right from the God of the Old Testament ? Has there ever been a race-people-nation on the face of the earth more proudly self-identifying as identical down the ages ? Originally raised by God to cradle the Messiah, alas, when he came they refused, collectively, to recognize him. Collectively also, meaning there are always noble exceptions, they have remained faithful to that rejection, so that they changed their religion from that of Abraham and Moses and the Old Testament to that of Anas, Caiphas and the Talmud. Tragically, their very messianic training by God drives them to go on rejecting the one whom they hold to be a false messiah. Until they convert at the end of the world, as the Church has always taught they will do (cf. Rom. XI, 26-27), they seem bound to choose to go on acting, collectively, as enemies of the true Messiah.