Matthew 27:25:Now at the feast the governor was accustomed to release for the people any one prisoner whom they wanted. At that time they were holding a notorious prisoner, called Barabbas. So when the people gathered together, Pilate said to them, “Whom do you want me to release for you? Barabbas, or Jesus who is called Christ?” For he knew that because of envy they had handed Him over.
While he was sitting on the judgment seat, his wife sent him a message, saying, “Have nothing to do with that righteous Man; for last night I suffered greatly in a dream because of Him.” But the chief priests and the elders persuaded the crowds to ask for Barabbas and to put Jesus to death. But the governor said to them, “Which of the two do you want me to release for you?” And they said, “Barabbas.” Pilate *said to them, “Then what shall I do with Jesus who is called Christ?” They all *said, “Crucify Him!” And he said, “Why, what evil has He done?” But they kept shouting all the more, saying, “Crucify Him!”
When Pilate saw that he was accomplishing nothing, but rather that a riot was starting, he took water and washed his hands in front of the crowd, saying, “I am innocent of this Man’s blood; see to that yourselves.” And all the people said, “His blood shall be on us and on our children!” Then he released Barabbas for them; but after having Jesus scourged, he handed Him over to be crucified.
(Matthew 27:15-26, NASB)
That seems like a very strange thing for a lynch mob to say. Most lynch mobs I've ever heard of have been the opposite, convinced not of their guilt but that their targets deserved their fates. US lynchers sometimes took pictures of their handiwork, and some US politicians tried to protect them, blocking efforts at Federal anti-lynching laws. When Muammar Khadafy was lynched by some militiamen, a militia commander said about that "What are we supposed to do? Kiss his head?" In fairness, some of them drew the line at how one militiaman broke the news to his daughter Aisha who had called him on his cellphone: "It's over. Ol' Fuzzhead (Abu Shafshufa) is dead". They considered it rude and disrespectful.And all the people said, “His blood shall be on us and on our children!”
Even worse, if they were willing to accept blame for executing Jesus Christ, then why should their descendants also have that blame? Their descendants had not been involved, and the only problem with them is if they defend those Jesus-crucifying ancestors of theirs.