The real reason that practicing Jews can't be Zionists is because as Hillel pointed out: "What is hateful to you, do not do to your fellow: this is the whole Torah..." Ergo Jews are, if anything at all religiously or morally (like Christians and Muslims etc), followers of the golden rule.
On the persistence of culture and ancestry, when in my twenties I once met this old couple who told me they were Greek. I knew lots of Greeks so I asked him where in Greece, thinking we might know people in common from Athens or Crete or Cyprus. He replied: "...Egypt." Foolishly assuming he was a child of merchants I said " So when did your family settle in Egypt, Seraphim? " The lovely old man looked at me with a slightly mischievous glint in his eye and replied "Oh...I think it was about two thousand years ago or so..."
-On identity, that's what you are missing.