There are some Jewish skeptics out there that go beyond my skeptical views in questioning the validity of the Jewish religion and go to questioning the validity of the concept of a Jewish people. See, I think they come to the issue as thinking of the assertion of there being a "Jewish people" as being a religious belief itself. If the concept of a "Jewish people" is founded in Judaism, then that concept should fall just like the rest of the religious assertions.
Compare Judaism to Mormonism (I know I'm not the first to do it). In Mormonism there is the idea that they are members of the tribes of Israel either through descent or adoption. It is their religious belief which is the foundation for their understanding of their own peoplehood. Is Judaism like this too? Or is Jewish Peoplehood a concept found outside of the Jewish religion?
If you're Jewish, take a look at your skin. Is it the dark olive color typical of Semitic groups or of people from around the Mediterranean? I doubt it. So in terms of direct descent most Jews today probably have an only minimal genetic connection to the original Israelite stock, if that. Yet from recent genetic tests and studies of Jewish groups around the world, there is still a measurable genetic connection and Jews from opposite sides of the Earth are often more closely related to each other than to the non-Jewish people they live among.
But is it genes that make a people? Genetics are very flexible in terms of who is in the group vs outside the group. We can hardly define human races genetically, so it would really be an exercise in futility to try and define genetic markers for Jewishness. The genes are useful though. They tell us that there is a measurable biological connection among Jews and establish a common source. But in what sense are Jews a people?
If we look back in history (yes, we can use Tanach reliably here) we see that the Israelites were hardly religiously uniform. There were idolaters and polytheists but they were still considered Israelites. They didn’t lose that birthright by not being devoted to YHVH. This consideration extended through the entire time of Jewish development. It is ingrained in the Oral Law that even heretics and apostates are Jews. The very name "Jews" is directed towards the people of Judah, not the belief system that those residents held. The Jews as a People are not religiously defined, but naturally.
To be part of one group there must be something which sets your group apart from all others. The most obvious trait among the Jewish people through history is obviously religion. But if you reject the religion is that all the group has which holds it together? I don’t think so.
There is a Jewish culture, Jewish history, Jewish tradition, Jewish music, Jewish folk tales, Jewish texts, Jewish legends, Jewish foods, Jewish jokes, etc. There’s a lot of Jewish stuff out there besides religious faith and devotion. And I think one is fully justified to say that there is a Jewish people even while not believing that the Jewish religion is true.
In the super-skeptics view it is the Jewish religion which created the Jewish people. In my view it is the Jewish people who created the Jewish religion.