Biblical Jews - Modern Jews... Is there a difference?

Who is a Jew? Is it a certain religion that makes a person a Jew, or is it the natural bloodline? If one is a Jew by definition of modern Judaism, is that same person a Jew, Biblically speaking? If a person is a Jew by modern definition but not by Biblical definition, would Bible prophecy concerning 'Jews' apply? Are there actual Bible prophecies which specifically concern 'Jews'?
These questions may seem ridiculously simple and unimportant, but bear with me, as I present a case for investing serious thought and research into answering them.
In the Bible, the remnant of the southern Kingdom of Judah, consisting of the descendants of the Tribes of Judah and Benjamin, were the first to be called "Jews". The northern Kingdom of Israel, comprising the other ten Tribes, had been dispersed and forever melded into the pagan societies of the world, 700 years before Christ. They were rejected by the Lord, who had "afflicted them, and delivered them into the hand of plunderers, until He had cast them from His sight" (2 Kings 17:20). About 586 BC, Judah was taken into Babylonian captivity, until 538 BC, when the remaining 'Jews' were released and allowed to return to their homeland, where they ultimately came under Roman government until Jerusalem was totally destroyed by Titus, in 70 AD.
During Old Testament times, one was a natural 'Jew' by virtue of birth. His or her father had to be a Jew, which is the only way the lineage could be traced. According to modern Judaism, this is not the case. One is a natural-born Jew today, only if his or her mother is Jewish, making it impossible to trace one's lineage back to the patriarchs.
In Bible times, one could also be called a 'Jew' if he were a "proselyte"--a Jew, not by birth, but by virtue of circumcision and adherence to the law. Circumcision is also required in modern Judaism, but circumcision alone, was never enough according to the Old Testament, for one to become a member of the household of Israel. All of Abraham's physical descendants circumcised the male children in obedience to the command passed down by Abraham. This practice was followed not only by Isaac and his seed, but the descendants of Ishmael, as well as the descendants of Abraham's six sons by his second wife, and the descendants of his sons by concubines--all of them, including Muslims today, practice the rite of circumcision. But circumcision does not, nor did it ever, make them 'Jews'.
Adherence to the law of Moses, which was a strict requirement for the Jews of old, is not required by even the strictest of orthodox Jews today. If the Jews of old ceased to cooperate with God's method of atonement--the blood sacrifices--they were 'cut off' and no longer in covenant with God. Today, those Old Testament laws and ordinances have been replaced in modern Judaism by the Talmud--the 'oral traditions'. Thus, modern Judaism has absolutely no validity. Nor, did it ever. Even if the Messiah had never come and the Old Covenant was still in effect, the Jews of today would be completely outside that covenant, and without any relationship with God.

Jews in the time of Christ...

By the time of Christ, the term "Jews" usually referred to those who strictly adhered to the religious laws and ordinances. While it is true that Jesus was a Jew, the disciples were Jews, and the multitudes to whom they preached were Jews; nearly every reference to "the Jews" in the New Testament was concerning the religious leaders, not the Jews-by-birth. Examples include statements such as, "When the Jews saw the multitudes", or "the Jews sought to kill Him (Jesus)", or "the disciples were in fear of the Jews", etc.
The number of references to "Jews" in the Gospels and the Book of Acts far exceed the number of references in the rest of the New Testament. And though many are preaching today about the 'Jews in Bible prophecy'; even the Book of The Revelation makes no reference to "Jews", except in the letters to the seven churches (Chapters 2 & 3). And in those letters, Jesus only mentions those "who say they are Jews and are not" and He calls them the "synagogue of Satan" (Rev. 2:9, 3:9).
No Bible prophecy concerning the latter days, Old Testament or New Testament, includes any mention of "Jews". Prophecies do mention "Israel", but there is a difference. The "Jews" refer simply to those of the religion of 'Judaism'. "Israel", on the other hand, refers to the seed of Abraham--the chosen people of God. The only 'Israel' in Biblical, end-time prophecy, comprises those who are also described as having a "new heart", "righteous", "saints"; those who have "the testimony of Christ", those who "follow the Lamb", etc. Another name for them would be "Christians".
What about this "synagogue of Satan"? To whom was Jesus referring, and is there a valid application today?
Consider this... By the time the aged apostle John heard those words from the resurrected Lord Jesus, he had been banished to the Isle of Patmos and nearly all of those with whom he had once enjoyed fellowship had gone on to glory. Decades before, the young apostle was one of the 120 Jews who believed in Jesus and were gathered in an 'upper room'. They were 'in one mind and one accord', waiting for the 'promise of the Father'--the outpouring of the Holy Spirit.
With a roaring sound and the manifestation of flames of fire upon each of them, the Holy Spirit filled the house and everyone in it. The first part of the remnant of Israel had received a new heart and a new spirit within... They had been fully cleansed of their iniquity and God had become their God, and they, His people.
This band of 120 believers went immediately to the streets of Jerusalem and began to preach Jesus and the resurrection. On that very day, three thousand Jews came to Christ (Acts 2:41). A few days later, Peter had another opportunity to preach the gospel of Jesus to another large crowd of Jews. The result? Five thousand men, plus women and children became believers. What did they call these thousands of Jews who were coming to Christ? At first they simply called them "believers" (Acts 5:14). Then they called them people of "the Way" (Acts 9:2). Finally, at Antioch, a name was given to them that stuck--"Christians" (Acts 11:26). The Jewish king Agrippa was obviously familiar with the term, as he accused the apostle Paul of attempting to persuade him to become a "Christian" and Paul readily admitted to the same (Acts 26:28-29). Even the apostle Peter used the term "Christian" referring to himself and other believers (1 Peter 4:16). The name change was no accident. It was in fulfillment of prophecy... "You shall be called by a new name, which the mouth of the Lord will name" (Isaiah 62:2).
The apostle John witnessed this and was a vital participant in all of it. And in the years that followed, John ministered the Word, just as Jesus had commanded, first to Judea (the Jews), then to Samaria and beyond. Many of the Jews believed John's message and became Christians. Some did not believe and ultimately died in their sin. It was the latter, John referred to when he wrote... "They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us (1 John 2:19).
Further addressing the true nature of these Jews of his day who had ultimately rejected Christ, he wrote... "Who is a liar but he who denies that Jesus is the Christ? He is antichrist who denies the Father and the Son. Whoever denies the Son does not have the Father either; he who acknowledges the Son has the Father also." (1 John 2:22-23)
Keep in mind, these were Jews who actually lived while the Old Covenant was still in effect. They had heard the New Covenant preached and had plenty of opportunity to believe and receive Christ--but they were obviously not (as John explained) true 'Israel'--they were not the 'elect'. They were Jews by blood or religion only, circumcised of the flesh, but not the heart--as Paul also explained, "They are not all Israel who are of Israel" (Romans 9:6).
None of the Jews who once were legally in covenant with God through the law, were automatically covered by the New Covenant... It had to be by faith. The Old Covenant was made obsolete when the New was established (Hebrews 8:13), thus, anyone who rejected the offer of the New Covenant remained uncovered--without hope of salvation or any relationship with God. And to continue to claim covenant with God was tantamount to 'blasphemy'. It was undoubtedly these, who continued calling themselves "Jews", even though they had completely rejected the King of the Jews, that Jesus renamed "the synagogue of Satan" and judged them blasphemers.
Jesus had confronted that same spirit, manifest in the Scribes and Pharisees. They were, physically speaking, just as much the 'seed of Abraham' as anyone. Jesus acknowledged this. But He also told them that in reality--in the way God sees it--they were NOT Abraham's children, nor were they God's children. Their father was not God--their father was the devil (John 8:37-44). In other words, they were also, "the synagogue of Satan". Why? His explanation was so simple, yet they did not want to hear it; and few want to hear it to this very day...
"And He said to them, You are from beneath; I am from above, You are of this world; I am not of this world. Therefore I said to you that you will die in your sins; for if you do not believe that I am He, you will die in your sins." (John 8:23-24).
According to the New Testament, no one who rejected Jesus christ would have any part in the Kingdom of god. The warning was clear--even the warning written specifically to the Hebrew people--saying that to go on in sin (instead of coming to Christ for salvation) means that "there no longer remains a sacrifice for sins, but a certain fearful expectation of judgment, and fiery indignation..." (Hebrews 10:26-27).
The significance of this warning being directed especially to the Jews in this case, is even more apparent as the warning continues...
"Anyone who has rejected Moses' law dies without mercy on the testimony of two or three witnesses. Of how much worse punishment, do you suppose, will he be thought worthy who has trampled the Son of God underfoot, counted the blood of the covenant by which he was sanctified a common thing, and insulted the Spirit of grace? For we know Him who said, 'Vengeance is mine, I will repay,' says the Lord. And again, 'The Lord will judge His people" (Hebrews 10:28-30).
The Jews, to whom, "Hebrews" was written, once had a covenant with God through Moses. That covenant was now obsolete ("In that He says, 'a new covenant', He has made the first obsolete..." --Hebrews 8:13). And unless they repented, acknowledged the Truth, and received Jesus as Lord and Savior, they could expect nothing but "judgment and fiery indignation". Today, there are those who are called Jews, but receive no such warnings from many who know the Lord. Well known church leaders, such as Rev. John Hagee, pastor of Cornerstone Church in san Antonio, Texas, teach thousands of Christians that the Jews should not be 'targeted for conversion'--that preaching the gospel to them is wrong--that they have a covenant with God through Moses, which is still in effect...
If I may borrow one of Pastor Hagee's favorite phrases... "He is exactly wrong!"
No person living on earth today is under the Mosaic Covenant unless that person is two thousand years old! What part of "ob-so-lete" does Brother Hagee and so many others not understand? "Obsolete" is part of the core of the message written to Jews who were old enough to have been under the Old Covenant, and the message was loud and clear to them--The Old Covenant is no longer an option... It's the New Covenant, or No Covenant.
Why is our message not as loud and clear to Jews today, who have never been under any covenant with God to begin with?