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>> “The same Jesus of the same gospel was offered freely to both Jew and Gentile alike, throughout the whole Bible” <<
This statement is essentially gibberish.
“Jews” are followers of Phariseeism. Jews didn’t exist until the second temple period. Did you mean Israelites, or Hebrews?
By Biblical definition, “Israel” is the believing remnant of the descendants of Jacob, and those that sojourn with them. That term covers all who have believed, and will believe, until Yeshua gathers us at the Day of Trumpets. They are his Kehillah, or Assembly.
(often mistakenly called a “church.”)
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What about the term "Mordecai the Jew" used in the OT book of Esther (see Esther 5:13; 8:7; 9:29; 10:3)? The Hebrew word used was "Yehudi" which means: Jewish (see http://biblehub.com/hebrew/3064.htm).