You're conflating different things. Jewish society was both patrilineal and largely patriarchal, but not when it came to "who is a Jew". If you were in the right forum (Same Faith Debates), which you are not, I'd press you on how is it that you supposedly know that the Bible (your Bible, I assume) supposedly squeezes out the other texts.
BTW, I really don't likely think any of us here are really interested in your concept of "salvation".
1. So you are admitting the Bible does go on the patriarchal line for who is Jewish?
2. And we can start with which of the following:
*Tanakh
*Talmud
*Zohar
*Apocrypha
*etc. etc.
Says in it thousands of times,
thousands of times, "...hear... obey... listen to... the word of the Lord... the word of G_d."
3. Have I told you my concept of "salvation"? How do you know you aren't really interested in it? Are you uninterested in salvation from a Jewish, not Gentile, Messiah? Not an imam, not an avatar, not a guru, not a mere Rabbi or Kohen or even a Kohen Gadol, but the very logos/ethos of Ha Shem? I bet you are interested--not that I'm looking to proselytize--but since you mentioned it:
a) There are many good Jewish people in this world
b) There are no perfect Jewish people, me included
c) After all, being sort of/striving to be perfect is like being a "little pregnant" or "a little dead" or "a little born again"
d) Messiah offers perfection to all who trust Him--after all, in the world to come, if you hurt another, it isn't the glorious Olam HaBa
e) Who is this Messiah? ...is what I'm asking, if you don't mind my asking...?
f) Baruch Ha Shem!