The word Jews has two meanings - one is religion and another is a nation ("race").
Same way with Armenians - there is an Armenian Church and Armenian nation. Still after you convert to Armenian Christinity you can marry with an Amermenian, absorb Armenian culture and in the way you will become the part of Armenian ethnic community.
Sometimes it is hard to distinguish ethnicity and religion but many Jews are atheists, especially in Israel and they see themselves as very Jewish.
And no A.J., I was not calling you a racist. Most of that post was written not only to address your statement, but that of many others on the thread as well, including those of "racists". :^)
The takeaway from my position is that arguing over what a Jew is, without clearly defining what one means by "Jew" is a waste of time.