Does being Jewish have any meaning outside of religion?

Yes, it would be silly to say that Baptists are a race. Because then you would be looking at race as a social construct.

Jews are a "race" in the sense that the majority share genes, if you will, that show their ancestors originated from a particular region of the world. Jews are not the only ones who share these particular markers.

The article Billvon linked explains it quite well.

Boiled down to its essence, race equates to “region of ancestral origin.”

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Religion in that sense, should not matter. Sadly for some it does.

For example, those genetic markers and predispositions to certain diseases that so many Jews share, are also shared by many Palestinians.

The DNA that tightly links Ashkenazi, Sephardi and Mizrahi, three prominent culturally and geographically distinct Jewish groups, could be used to support Zionist territorial claims — except, as Ostrer points out, some of the same markers can be found in Palestinians, our distant genetic cousins, as well.​

The reason for this is simple.

On the male side, or male genetic line, if you will, the similarities between people originating from that region are exceptionally strong. They are not as strong on the maternal side. Hence why they share so many, but not all.

Another team, lead by Almut Nebel at the Hebrew University, Jerusalem, took a closer look in 2001. They found that Jewish lineages essentially bracket Muslim Kurds, but they were also very closely related to Palestinians. In fact, what their analysis suggested was that Palestinians were identical to Jews, but with a small mix of Arab genes – what you would expect if they were originally from the same stock, but that Palestinians had mixed a little with Arab immigrants. They conclude:

We propose that the Y chromosomes in Palestinian Arabs and Bedouin represent, to a large extent, early lineages derived from the Neolithic inhabitants of the area and additional lineages from more-recent population movements. The early lineages are part of the common chromosome pool shared with Jews (Nebel et al. 2000). According to our working model, the more-recent migrations were mostly from the Arabian Peninsula…​

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In 2008, a more sophisticated analysis was published that made use of whole mitochondrial DNA sequences. They found no evidence for the genetic bottle necks that indicate founding mothers in the large Jewish populations. Instead, they found a complicated picture with a very diverse gene pool suggesting intermarriage both with local populations and other Jewish groups.

The overall conclusion is that the female Jewish line deviates a lot more from the Palestinian heritage than the male line, but the heritage is still there.​

Hence why they share some of the same markers.

Being able to understand this is exceptionally important, not to view race as a social construct or for political value or gain, but to understand it for medical reasons in particular. It has nothing to do with religious superiority or even racial superiority. And in a broader context, it is a way to trace our links to our ancestors and from an archaeological perspective, it helps us understand the history of homo sapiens as a whole, because it helps us understand our origins.

This does not just apply to Jews and Palestinians, but for understanding race as a point of "region of ancestral origin" because in some cases, it can mean the difference between life and death in the medicine and treatments doctors prescribe.

Certainly, some will want to and do to use such genetic distinctions for political or religious gain, but they would be wrong to do so.