No, I think it's absurd to have a religion linked into ethnicity and I find the whole jewish is it a religion or is it an ethnicity question very confusing. I'd love a conclusive answer but as far as I can tell there doesn't appear to really be one.

There are several ethnicities (Ashkenazim, Sephardim, etc.) which are historically Jewish, just as there are several ethnicities (Irish, Hispanic, etc.) which are historically Catholic. When someone says they are ethnically Jewish it generally means they belong to one of those ethnicities, and grew up with the associated foods, festivals and other cultural influences.

Sure, but Spanish and Irish atheists don't refer to themselves as atheistic catholics, whereas I have heard jewish friends of mine refer to themselves as atheistic jews.

But the term atheist Jew is just a proxy for atheist Ashkenazi or atheist Sephardi. Which is no different from atheist Irishman or atheist Spaniard.

Jewishness is a combination of religious, ethnic, and cultural factors. There's a lot of typically "Jewish" thought, for example, that is not religious.