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The theory that the Jews were conspiring to sacrifice Christian children had started to spread in the 11th century. The legend proliferated first in England and then in France. [2].
Martin Luther in his early days naively imagining that the Jews, to whom he was attracted by his studies, would flock to the Church in his reformed version. When nothing of the sort happened, he denounced them in a set of pamphlets written in vituperative fury. He had produced the early, favorable "That Christ Was Born a Jew" in 1523, but after he turned on this so-called "damned, rejected race," he wrote Against the Sabbatarians (1538) and On the Jews and Their Lies (1543) [3].
[0] https://en.wikipedia.org/wiki/Antisemitism_in_Europe
[1] https://en.wikipedia.org/wiki/Antisemitism_in_Christianity
[2] https://www.swissinfo.ch/eng/culture/how-christian-europe-cr...
[3] https://www.ushmm.org/research/about-the-mandel-center/initi...
Of course, this sadly does not stop some people from being antisemitic, especially if you go back a few centuries. But for them, the Bible has a few paragraphs (Romans 11:11–32) specifically explaining why it is wrong for Gentile Christians to think that they are somehow "better" than the Israelites. For example, it was only through ancient Israel's rejection of Jesus that Paul (himself a Jew) went to preach to the Gentiles in the first place, and thus arrogance is unwarranted. Also, God will still save Israel in the end and has not abandoned them. To me, this last point feels like a slam dunk case against anyone who calls themselves a Christian and yet is antisemitic—why would a follower of God hate those whom God wants to save?[0]
All this to say, I think that Christianity's own scripture preaches the exact opposite of antisemitism, and so it's inaccurate to call Christianity "antisemitic on a rather deep level."
[0] Frankly, this applies more generally to Christian attitudes towards non-Christians in general. We have no grounds to be holier-than-thou, since no one is saved by their own goodness. And yet, at least on the internet, there's a general perception that that's how (American) Christians are towards others. That is precisely the opposite of what Jesus did (Mark 2:16–17), and He actually was holier than the rest of us.