This is one of those topics that is somewhat like the saying, "beauty is in the eye of the beholder," as there are several ways to define the word "Jew," and depending on the beholder all the answers may be correct.
1) I was born a Jew and am a descendant of the House of Aaron, (which in my little mind doesn't make me special as Aaron sort of encouraged people to make this golden calf). But in that regard what Hezekiah Ben Israel shared was "What defines a Jew from a Gentile is the Tribe the Jew is from. The Jew is a Jew because of the Nation of Judah, which were the Tribes of Benjamin and Judah. Judaism is a religion that the Edomites got from the Nebateans.." is very correct.
2) As stated, "Judaism is a religion that the Edomites got from the Nebateans.." is also correct as it is a religion.
3) Another very loose definition of a "Jew" is simply one of God's people, which many that are in Christianity might disagree with as Christianity simply by the name leads one to believe that the Jew was replaced by a Christian, but if one does not believe that Jesus came to start a new concept called Christianity and came so that all could be "grafted into the promise," then that would fit the definition of "Jew" meaning simply one of God's people.
I personally go with the definition of "Jew" simply being one of God's people. I think just in personal experience, we tend to like to label things, which tends to allow us to identify with something or a group, but who we are really supposed to identify with is being a child of God. Jesus/ Yeshua which ever you prefer was I believe to be the work of the Holy Spirit through Mary, which came to show us all those that came after Him and those that came from the blood line, how to have access with God so that we may walk with God as Adam did, which unfortunately is not often taught and as a result most of us do not have a clue as to what we were given.
Which blood is more important to us, the blood of Christ which is two very important parts, which is Jesus or Yeshua being the head of Christ and secondly, but hopefully attached is the body of Christ. One cannot accept one without the other. One cannot accept the head and reject the body and if one does then they are not able to discern the body of Christ and sleep. One either accepts that blood or they feel their parents blood is more significant and I think at least we are here to make that choice, which is more important.
I think where some of the confusion comes from is that one likes to know who is saved, which takes us back to the labels. If one does not know of Christ am I to say they were not of God or saved? I personally believe only God can call that one. God knows the heart of everyone. We might have our guesses or beliefs, but that may not even close to reality. There are some that say there is no God, but all those that believe there is a God all here from God at one point or another (otherwise no one would ever go to an alter call). There are also spirits that also come into play, which tend to take people down different paths in life.
We all believe that what we think we know is truth, but the real truth is the proof and that is always in the pudding.