No, this is not correct. There are people who go to church and use Jesus as a central moral figure, partake in many or all of the rituals, who nevertheless do not believe in god. Often you find this runs in families, because the intellectual tradition is that it’s fine to go to church and like Jesus, but reject any or all of the supernatural parts or moral teachings.

Then you have people that may have grown up surrounded by some of the trappings of Christianity, but because of their atheism, do not attend church and take part in only the most universal rituals (Christmas, basically, and even then, the Christian bits are mainly removed). Christian thought is not the moral or philosophical touchstone.

> "atheist Jews" can exist only because they exist in the cultural Christian west

There are atheist Jews in Israel. Is Israel part of the "cultural Christian west"?

The parent poster is more arguing that the atheist Jew label only really exists because most of the atheists in the US are Christian atheists to a certain extent (in that they celebrate Christian holidays and many aspects of Christian culture).

So you need to explicitly define atheist Jews as the exception.

Approximately 10% of the Israeli population identifies as "atheist Jews" (more than that are non-religious, but only a minority of non-religious people embrace the 'atheist' label)

I don't see how the identity of atheist Jews in Israel depends on non-Jewish people celebrating Christian holidays in the US (whether those people identify as atheists or not)