When salvation and the Gospel are seen in the context of God's covenant with a particular people (Israel and the Church), to set the world to rights and reflect the coming kingdom of God, the horizontal dimension emerges as not just an implication, or an add-on, but as an organic, dynamic, and natural aspect of the Gospel in its entirety.
The Gospel is really the whole story of God's gracious action in and for the world, most centrally, of course in the person of Jesus, the Messiah. The call of the church, then, is to proclaim this story and to invite the world to enter into this story of redemption -- to trust in God, to proclaim Christ's Lordship, and join in the project of redeeming and reconciling all of creation. On the corporate, communal level, reconciliation with God becomes, by natural extension, reconciliation with others. "There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus" (Gal. 3:28).
Justification by faith, as an essential component of the larger, fully-orbed Gospel, levels the playing field. It is by grace alone through faith alone in the context of God's covenant with creation (originally) and with God's people (secondarily) that we find our true place and purpose in the world. The only real hope for genuine reconciliation with the "other" (rich and poor, black and white, male and female, conservative and liberal, gay and straight, etc.) is Christ's sacrifice on behalf of and for sinners. As the apostle Paul put it,
.