What is a Jew? What does it mean for someone to be Jewish?

I find a phrase used in an article that I just read to be very confusing, perplexing, and disturbing!
And yet, I have come across many people during my 68 years that have often used the same type of phrase.
The phrase in the article that confuses me, that perplexes me, that disturbs me is:
"but he was more Jewish than Polish."

ref: Bernie's Religion Is the Revolution

Why do people say such a things? Why do people write such a thing?
I never hear anyone say or read anyone write:
"she is more Christian than Polish" or "he is more Lutheran than German" or "she is more Catholic than Italian"
Can anyone explain the use of this type of phraseology to me? Will anyone tell me why this is done?

And while I am at it, why do people say "you don't look Jewish" or "that sounds like a Jewish name" or such things? Why do some people refer to Jewish people as a race or as a nationality or anything other than a religion? And why do some people have the idea that all people of the Jewish religion have the same religious beliefs and practices and fail to recognize there are a variety of Jewish denominations?

I have written other Roland Hansen Commentary entries concerning Jewish as a topic or theme.

I have written other blog entries concerning Jewish as a topic or theme in Roland's Ramblings.

There are many, many interesting articles to the question of What is a Jew? all over the internet.