I don't really see people talking about how cultural Christianity is applied to Jews.
In Christianity, Jews are the people who rejected and betrayed Jesus and are punished with statelessness and destitution, whose only redemption is accepting the Messiah and the Son of God. This is the basis of several antisemitic tropes, most prominently deception, religious supercessionism and the Wandering Jew.
In cultural Christianity, these tropes are considered tenants of Judaism rather than Christianity, as Judaism is considered Christianity without Jesus.
Christians see themselves as tortured saints, persecuted for spreading the truth of Jesus and God across the globe. Missionaries who go to non-Christian lands to try and get the people to convert by fearmongering with damnation to Hell see themselves as victims when they're rebuffed and asked to stop.
Cultural Christian non-Christians are usually atheists and adherents of folk religion revivalist movements who have suffered religious abuse, as many sects of Christianity normalize emotional abuse by instilling inherent guilt in the Original Sin and even physical abuse in "Spare the rod; spoil the child". These cultural Christians see the millennia of antisemitism and roll their eyes, to them we're just another sect of delusional religious people with a persecution complex.
To become a Christian all you need to do is accept the Father Son and Holy Spirit, to affirm your beliefs and confess your sins. To become a Jew you are either born a Jew, or you learn the Jewish culture and religion for months on end and must live half a year under the strictest restrictions of the Jewish lifestyle to show commitment. That is the difference between a universal religion and an ethnoreligion.
In a Culturally Christian world there is no room for ethnoreligions, and they do not exist. All religions are about your faith and which God(s) you believe in. So in a Cultural Christian's eyes, a country of Jews is a country that holds one faith supreme above all others and conditions rights with conversion, as that's how Christian countries have historically been.
Christianity's common ground with Jews comes from the Roman Empire appropriating the religion from the Cult of Jesus, and making it more appealing to the masses by introducing Greco-Roman and Germanic folk religion aspects into it. Xmas is Yule but with Jesus, Easter is a fertility holiday but with Jesus and so on. In the eyes of the Cultural Christian, Christianity and Judaism are two once-antagonistic sects of the same religion, no different than Catholics and Protestants.
Cultural Christianity erases and appropriates Judaism and is as inherently hateful of Jews as religious Christianity.
Now, when it comes to the elephant in the room: Islam.
Islam, like Christianity, is a universal religion. You must believe in Allah and accept the prophets, which include both Jesus and Muhammad. It is no more inherently violent than Christianity, though it's no less. In the Christian's eyes, Islam is the competitor, the enemy. The Muslims conquered Christian lands and converted them, and they've fought holy wars against one another throughout the Middle Ages.
To become a Muslim the Cultural Christian doesn't need to unlearn any of the core tenets of their culture. They can simply apply it to Islam.
Which is why many Cultural Christians, damaged by Christianity, are sympathetic to Islam. And since Muslims and Jews are no longer on good terms, they use this sympathy to give themselves a free pass to be antisemitic. Whether Muslims check their converts for bigotry, allow it or are powerless to stop them, that's another issue.
Jews are not diet Christians. We have less in common with you than you have with Muslims. Unlearn Christian cultural appropriation.
And no, I don't care that it's "offensive" to associate you with Christianity due to the religious abuse you endured. You still see the world through a Christian lens.