Why did God choose a people at all?
Biblical theology has no more basic question, because the answer determines what a congregation is for. If God chose a people for their own sake, to be his special possession walled off from the world, then a closed, inward-facing church is faithful. If God chose a people for the sake of everyone else, then a closed church has inverted the reason it exists.
The Scriptures answer the question in the first sentence of election and give the same answer every time after.
The purpose clause in the first promise
Now the LORD had said unto Abram, Get thee out of thy country... And I will make of thee a great nation, and I will bless thee, and make thy name great; and thou shalt be a blessing... and in thee shall all families of the earth be blessed. (Genesis 12:1-3)
Abraham is chosen, and the sentence runs on past his choosing into a purpose clause about everybody else, all families of the earth. The election of one man is stated, in its founding text, as the means of blessing all.
The promise is repeated to Abraham again (Genesis 18:18; 22:18), to Isaac (26:4) and to Jacob (28:14), with the same clause every time. The promise never appears without the nations attached to it. The first thing to know about the chosen people is that they were chosen for the unchosen.
A kingdom of priests
At Sinai, the nation receives its constitution:
Ye shall be unto me a kingdom of priests, and an holy nation. (Exodus 19:6)
A priest stands between God and people who aren't priests. A whole nation of priests only makes sense if there's a congregation for them to serve, which in Israel's case is the nations. Israel's constitution is priestly, so it faces outward the way every priesthood does.
Then Moses tells them why the law-shaped life matters: this is your wisdom and your understanding in the sight of the nations, which shall hear all these statutes, and say, Surely this great nation is a wise and understanding people (Deuteronomy 4:6). The ordered common life exists to be observed by outsiders and to produce a conclusion in them.
The stranger in the temple's dedication prayer
When Solomon dedicates the temple, he prays for the foreigner:
Moreover concerning a stranger, that is not of thy people Israel, but cometh out of a far country for thy name's sake... hear thou in heaven thy dwelling place, and do according to all that the stranger calleth to thee for: that all people of the earth may know thy name. (1 Kings 8:41-43)
The outsider is written into the temple's opening prayer, and the building had a court for him. Isaiah tells us why when he says mine house shall be called an house of prayer for all people (Isaiah 56:7).
Jesus was angry about exactly this when he cleared the temple. He quotes that verse: Is it not written, My house shall be called of all nations the house of prayer? but ye have made it a den of thieves (Mark 11:17). The court of the Gentiles (the outsider's space) was the space that had been turned into a market. The first thing to be commercialized was the room for the stranger.
"A light thing"
The prophets make the outward purpose explicit, even embarrassing:
It is a light thing that thou shouldest be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give thee for a light to the Gentiles, that thou mayest be my salvation unto the end of the earth. (Isaiah 49:6)
A light thing. Restoring the chosen people is described as the smaller task, and the nations as the larger one.
Psalm 67 takes the priestly blessing itself (God be merciful unto us, and bless us; and cause his face to shine upon us) and attaches a purpose clause to it, that thy way may be known upon earth, thy saving health among all nations (Psalm 67:1-2). Bless us so that they will know. The blessing of the insider has the outsider as its object.
The record writes the outsiders into the family where nobody could miss them. Rahab of Jericho and Ruth of Moab stand in the line of David and of Christ (Matthew 1:5). Naaman the Syrian is healed (2 Kings 5), the widow of Zarephath is fed (1 Kings 17), and Nineveh is spared (Jonah 3) while a prophet sulks about it outside the walls.
Jesus says it first, and they try to kill him
In the synagogue at Nazareth, Jesus's first recorded sermon reminds the congregation that Elijah was sent to a widow in Sidon and not to any widow in Israel, and that Elisha healed a Syrian and not any leper in Israel (Luke 4:25-27). Both of them were outsiders. And all they in the synagogue... rose up, and thrust him out of the city, and led him unto the brow of the hill... that they might cast him down headlong (Luke 4:28-29).
Insiders find the outward purpose of election that offensive. The first thing he said in public produced an attempted killing.
His parables keep the shape. Many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven (Matthew 8:11). The outsider gets a seat at the table. In the great supper the invited refuse, and the master says go out into the highways and hedges, and compel them to come in, that my house may be filled (Luke 14:23). The purpose of the feast is a full house, filled with the uninvited. Other sheep I have, which are not of this fold: them also I must bring (John 10:16). And I, if I be lifted up from the earth, will draw all men unto me (John 12:32). The verb draw describes attraction.
In his last prayer, the family's unity is given a purpose clause aimed at the world, that they all may be one... that the world may believe (John 17:21). The oneness of the insiders is for the belief of the outsiders.
Paul: the promise to Abraham was the gospel
And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. (Galatians 3:8)
Genesis 12:3 is the gospel, preached in advance. Where we might call the blessing of the nations an implication of election, Paul says it is what the gospel is.
Paul describes the mechanism as attraction when he writes through their fall salvation is come unto the Gentiles, for to provoke them to jealousy (Romans 11:11). The outsider is drawn by seeing what the insider has. Once inside, he is household, with more standing than any guest: ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God (Ephesians 2:19); if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise (Galatians 3:29).
Peter closes the circle by applying the Sinai constitution to a congregation of former outsiders:
But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light: which in time past were not a people, but are now the people of God. (1 Peter 2:9-10)
The Sinai titles, kingdom of priests and holy nation, are now said of Gentiles. The outsiders have become the priestly people. The purpose clause appears again with that ye should shew forth, which is the language of display. Two verses later Peter writes of your good works, which they shall behold (2:12).
A city with the gates left open
The end of the story is a city:
And the nations of them which are saved shall walk in the light of it: and the kings of the earth do bring their glory and honour into it. And the gates of it shall not be shut at all by day: for there shall be no night there. (Revelation 21:24-25)
The gates are never shut. The eternal city is permanently open to entrants, who are a great multitude, which no man could number, of all nations (Revelation 7:9). Across the whole arc, the language for what God is doing is the language of family, as in bringing many sons unto glory (Hebrews 2:10) and the firstborn among many brethren (Romans 8:29).
What this means for your congregation
God chose a people in order to grow a family. The chosen are chosen to be the visible, attractive, open household through which the family grows. Election is centripetal in its call and centrifugal in its purpose.
That's why there's a "third door" of apologetics at all. You might suppose we need it because argument fails and something softer is called for, but the community was always the method, the thing outsiders were meant to see, be drawn to, and join.
So ask of your congregation: could an outsider find us? Could he see our common life from where he lives? Would there be a court for him, a space that hasn't been turned into a market? Is our unity aimed at the world's belief, or at our own comfort?
A congregation that's closed, homogeneous, inward-facing, and invisible to its neighbors has done worse than fail at outreach, because it has inverted the reason it was chosen. A program won't correct it, though Genesis 12:3 will when it is read again with the purpose clause restored.