Keep in mind that this is not restricted to card-carrying pew-sitting parishioners. The Catechism (Link) puts it well:
"Christ's Spirit uses these Churches and ecclesial communities as means of salvation, whose power derives from the fullness of grace and truth that Christ has entrusted to the Catholic Church. All these blessings come from Christ and lead to him, and are in themselves calls to "Catholic unity."
"Furthermore, many elements of sanctification and of truth are found outside the visible confines of the Catholic Church: the written Word of God; the life of grace; faith, hope, and charity, with the other interior gifts of the Holy Spirit, as well as visible elements.
You can easily see that that deals with the salvation of other Christians outside the membership rolls of a parish, yet not outside the Church (whether they know it or not.)
Saying "Who saves, God or the Church?" is analogous to saying, "Who saves, God or Christ?"
Christ IS God. The Church IS the Body of Christ.
The Apostles Creed tells us, He descended into Hades (to the realm of the Dead) and opened the portals to the Kingdom of God.
Chapter and verse, please.