In Matthew 27 the Jews say, "His blood be on us and our children." But isn't this just a case of Christian antisemitism? Would they really have said such words?

Yes, I believe they would. Their request, in asking for Jesus' death, is solemn, almost like an oath. They are saying, in effect, "We know what we are doing and take responsibility."

Against those who believe the Jews are still the enemies of God, or "Christ-killers," the following points speak loud and clear:

* Yes, the earlier speeches in Acts, addressed to the Jewish leadership, did charge them with a terrible crime. Yet we are all responsible for Jesus' death: he died for our sins, Jewish or otherwise. See 1 Corinthians 15:3, Hebrews 2:9, and many more passages.
* God extended an offer of forgiveness to the Jews in Acts 2:38, 3:17-26, etc. Thousands accepted this offer (Acts 2:41, 4:4, 21:20 etc.)
* That generation was punished for their rejection of the gospel (Matthew 23:31ff). This took place in 70 AD, when the Romans permanently destroyed the temple, disbanding the Old Testament system of priesthood and sacrifice. In other words, the request of Matthew 27:25 was answered in history, during the First Jewish War.
* The writer of Matthew was himself a Jew, and writing a gospel for fellow Jewish Christians.

In short, the N.T. is not antisemitic.