I came across Jonathan Edwards interesting incite into how a people group may be consider God's elect or chosen people, but also be enemies and outside of the universal visible Church. A more concise summary is in this Edward's document:
Misrepresentations Corrected, and Truth Vindicated, Ecclesiastical Writings WJE Online, Vol 12, page 453,
"[...] the main argument which I offered, to prove that the nation of Israel were called "God's people," and "covenant people," in another sense besides a being visible saints. [...] that 'tis manifest, that something diverse from being visible saints, is often intended by that nation's being called God's people, and that that nation, the family of "Israel according to the flesh," and not with regard to any moral and religious qualifications, were in some sense adopted by God, to be his peculiar and covenant people; from Romans 9:3-5, "I could wish myself accursed from Christ for my brethren according to the flesh; who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises; whose are the fathers," etc. I observed, that these privileges here mentioned, are spoken of as belonging to the Jews, "not now as visible saints, not as professors of the true religion, not as members of the visible church of Christ (which they did not belong to) but only as a people of such a nation, such a blood, such an external carnal relation to the patriarchs, their ancestors; Israelites, 'according to the flesh': inasmuch as the Apostle is speaking here of the unbelieving Jews, professed unbelievers, that were out of the Christian church, and open visible enemies to it; and such as had no right at all to the external privileges of Christ's people." I observed further, that in like manner "this Apostle in Romans 11:28-29 speaks of the same unbelieving Jews, that were enemies to the gospel, as in some respect an elect people, and interested in the calling, promises and covenants, God formerly gave their forefathers, and are still beloved for their sakes. 'As concerning the gospel, they are enemies for your sakes: But as touching the election, they are beloved for the fathers' sakes. For the gifts and calling of God are without repentance.
Edward's opinions in Misrepresentations Corrected are also mused upon in the source document, An Humble Inquery, adding more of the same thought:
An Humble Inquiry into the Rules of the Word of God, Concerning the Qualifications Requisite to a Complete Standing and Full Communion in the Visible Christian Church, Ecclesiastical Writings WJE Online, Vol 12, page 268ff,
"And with regard to the people of Israel, 'tis very manifest, that something diverse is oftentimes intended by that nation's being God's people, from their being visible saints, or visibly holy, or having those qualifications which are requisite in order to a due admission to the ecclesiastical privileges of such. That nation, that family of Israel according to the flesh, and with regard to that external and carnal qualification, were in some sense adopted by God to be his peculiar people, and his covenant people. This is not only evident by what has been already observed, but also indisputably manifest from Romans 9:2-5, "I have great heaviness and continual sorrow of heart; for I could wish that my self were accursed from Christ for my brethren, my kinsmen according to the flesh, who are Israelites, to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises; whose are the fathers; and of whom, concerning the flesh, Christ came."
'Tis to be noted, that the privileges here mentioned are spoken of as belonging to the Jews, not now as visible saints, not as professors of the true religion, not as members of the visible church of Christ; but only as people of such a nation, such a blood, such an external and carnal relation to the patriarchs their ancestors, Israelites, "according to the flesh." For the Apostle is speaking here of the unbelieving Jews, professed unbelievers, that were out of the Christian church, and open visible enemies to it, and such as had no right to the external privileges of Christ's people. So in Romans 11:28-29 this Apostle speaks of the same unbelieving Jews, as in some respect an elect people, and interested in the calling, promises and covenants God formerly gave to their forefathers, and as still beloved for their sakes. "As concerning the gospel, they are enemies for your sake; but as touching the election they are beloved for the fathers' sakes: for the gifts and calling of God are without repentance."
These things are in these places spoken of, not as privileges belonging to the Jews now as a people of the right religion, or in the true church of visible worshippers of God; but as a people of such a pedigree or blood; and that even after the ceasing of the Mosaic administration. But these were privileges more especially belonging to them under the Old Testament: they were a family that God had chosen in distinction from all others, to show special favor to above all other nations. 'Twas manifestly agreeable to God's design to constitute things so under the  Old Testament, that the means of grace and spiritual privileges and blessing should be, though not wholly, yet in a great measure confined to a particular family, much more than those privileges and blessings are confined to any posterity or blood now under the gospel.
God did purposely so order things that that nation should by these favours be distinguished, not only from those who were not professors of the worship of the true God but also in a great measure from other nations by a wall of separation that he made. This was not merely a wall of separation between professors and non-professors (such a wall of separation as this remains still in the days of the gospel) but between nation and nations.
God, if he pleases, may by his sovereignty annex his blessing, and in some measure fix it, for his own reasons, to a particular blood, as well as to a particular place or spot of ground, to a certain building, to a particular heap of stones, or altar of brass, to particular garments, and other external things. And 'tis evident, that he actually did affix his blessing to that particular external family of Jacob, very much as he did to the city of Jerusalem, that he chose to place his name there, and to Mount Zion where he commanded the blessing. God did not so affix his blessing to Jerusalem or Mount Zion, as to limit himself, either by confining the blessing wholly to that place, never to bestow it elsewhere; nor by obliging himself always to bestow it on those that sought him there; nor yet obliging himself never to withdraw his blessing from thence, by forsaking his dwelling place there, and leaving it to be a common or profane place: but he was pleased so to annex his blessing to that place, as to make it the seat of his blessing in a peculiar manner, in great distinction from other places. In like manner did he fix his blessing to that blood or progeny of Jacob. It was a family which he delighted in, and which he blessed in a peculiar manner, and to which he in a great measure confined the blessing; but not so as to limit himself, or so as to oblige himself to bestow it on all of that blood, or not to bestow it on others that were not of that blood. He affixed his blessing to both these, both to the place and nation, by sovereign election (Psalms 132:13-15). He annexed and fixed his blessing to both by covenant. To that nation he fixed his blessing by his covenant with the patriarchs. Indeed the main thing, the substance and marrow of that covenant which God made with Abraham and the other patriarchs, was the covenant of grace, which is continued in these days of the gospel, and extends to all his spiritual seed, of the gentiles as well as Jews: but yet that covenant with the patriarchs contained other things that were as it were appendages to that great everlasting covenant of  grace, promises of lesser matters, subservient to the grand promise of the future seed, and typical of things appertaining to him. Such were those promises, that annexed the blessing to a particular country, viz. the land of Canaan, and a particular blood, viz. the progeny of Isaac and Jacob. Just so it was also as to the covenant God made with David that we have an account of, 2 Samuel 7 and Psalms 132. If we consider that covenant with regard to what the soul and marrow of it was, it was the covenant of grace: but there were other promises which were as it were appendages of things subservient to the grand covenant, and typical of its benefits; such were promises of the blessing to the nation of the literal Israel, and of continuing the temporal crown of Israel to David's posterity, and of fixing the blessing to Jerusalem or Mount Zion, as the place that he chose to set his name there. And in this sense it was that the very family of Jacob were God's people by covenant, or his covenant people, and his chosen people; yea and this even when they were no visible saints, when they were educated and lived in idolatry, and made no profession of the true religion.
On the whole, it is evident that the very nation of Israel, not as visible saints, but as the progeny of Jacob according to the flesh, were in some respect a chosen people, a people of God, a covenant people, an holy nation; even as Jerusalem was a chosen city, the city of God, an holy city, and a city that God had engaged by covenant to dwell in.
Thus a sovereign and all-wise God was pleased to ordain things with respect to the nation of Israel. Perhaps we may not be able to give all the reasons of such a constitution; but some of them seem to be pretty manifest; as, [...]
I would be interested if anyone had any thought about Karl Barth's understanding of Israel in Barthian Election, specially what he says in Dogmatics Volume II.2, the Doctrine of God
(Format and content editted for readability)
Related: an humble inquery, church, election, god's people, Jonathan Edwards, Karl Barth, misrepresentations corrected, olive branch, olive tree, romans 11