Gal 6:16 (NASB)- the Greek connective <kai> 'and' (instead of 'namely' or 'even') removes this one and only ambiguity in the NT. Elsewhere Israel is never anything but Israel and therefore 'Israel of God' refers to the believing remnant of Israel as distinct from the Church. See Romans 9-11 and especially Romans 11:1 to refute this false theology that has been so much associated with Christian antisemitism.
Note that "the new Israel" is not a biblical term. "I have discovered 77 instances in the NT where the words Israel or Israelite occur. ...Israel is never used in any other sense than Israel." (See D. Prince, 1992, pp. 15, 131-136).
Rom 9:6 this introduces the concept of the faithful remnant of Israel (see VII.A.4.a.)
Rom 11:19-20 in the context of the Letter to the Romans it is simply not possible to use this passage as a basis to justify 'Replacement Theology.' See Note on VII.B.1.