The church of Israel killed the Christ. Why should it be any different now. This woman was persecuted for Righteousness sake, which Jesus said would happen.
My understanding is that the death sentence was pronounced by the pagan Roman governor of Judea, Pontius Pilate, and not Jesus' faithful disciples of Israel. The Judeans who called for the execution of Jesus were not His "church"; they were unbelievers. And Israel was a separate kingdom from Judea.