Additional evidence to the contrary
From a Scriptural viewpoint the term "spiritual Israel" seems to be in good company although this term does not occur in the Bible. The following considerations need to be taken into account to understand why it is misleading and even dangerous to use the term "spiritual Israel."
Biblical language contrasts a number of material or physical things with spiritual ones such as the body (1Cor 15:44), drink (1Cor 10:4), food (1Cor 10:3), gifts (several passages), house (1Peter 2:5) and rock (1Cor 10:4). Certain physical objects are meant to be understood spiritually such as 'bread', 'light', 'water', 'crown,' 'throne' etc.. In all these cases the context makes it clear in which of the two ways a term needs to be understood. It is wrong to enumerate elements that are meant to be taken figuratively or spiritually and to conclude that therefore everything needs to be understood that way. Conversely it is equally wrong to understand everything literalistically literal without even looking at the context. To do so in either case is like picking the raisins out of a cake and then concluding that the whole cake consists of nothing but raisins. In all languages the nature of meaning is determined by context. Quite often, people who have never studied other languages do not understand this basic principle of meaning.
In Gal 4 Paul speaks of the "Jerusalem above" - to avoid any misunderstanding he plainly says he is using the term as a 'parable,' or in other words NOT literalistically literal - in order to draw a comparison. Comparisons often use figures of speech such as parables. We read of the "heavenly Jerusalem" in Hebrews 12:22 and in Rev 21:10 the "New Jerusalem" descends from above. In Revelation 17 even the city of Babylon - "the great harlot that sits on many waters" takes on a spiritual meaning and in Rev. 18 the term 'Babylon' is used in both ways, as a geographical town as well as a system in a spiritual sense.
This characteristic of all languages to speak in figurative or non-figurative ways would suggest that even though the Bible nowhere uses the term "Israel" in a spiritual way (except in Gal 6:16 not even in an extended but rather in a restrictive way, namely as the believing remnant of Israel, the Hebrew Christians/ the Messianic Jews) one might perhaps use it all the same. Some people are also using the term "new Israel" perhaps in parallel to the "new Jerusalem" (Rev 21:10) that descends from above but again, 'new Israel' is a coinage that is not found in the Bible. Gal 6:16 "the Israel of God" refers to the believing remnant of Israel, spiritual Israel in that restricted sense. And in that sense the believing Christian remnant of the Church that together with the believing remnant of Israel forms the spiritual body of Jesus Christ/Yeshua HaMashiah is also part of spiritual Israel. HOWEVER, the reason why the term 'spiritual Israel' can be very misleading and can even lead into dangerous heresy is that it can be falsely understood in the sense that Replacement Theology teaches: Israel has been replaced by the Church. This false doctrine is widespread and is as old as Christian anti-Semitism from which the Church needs to repent; it goes back to Justin Martyr (C.E. 165) who omitted the Jews from his 'Apologia' of the Christian faith. (Also see Key Issue #3 Israel and the Christians: replaced by the wild olive tree?).
See also the article by David Pawson, Israel in the New Testament (in a new window)
See also How is the term 'Israel' used in the New Testament? an article (in new window PDF Format) from the book Israelology-the Missing Link in Systematic Theology, by Arnold G. Fruchtenbaum.