I would contend otherwise-- that, in fact, our faith in the Gospel and our commitment to Christ's church are inseparable. This is an area where I hope/plan to do more thinking and writing in the next year or so. Meanwhile, here's a quote from John Calvin on the topic:
But as it is now our purpose to discourse of the visible Church, let us learn, from her single title of Mother, how useful, nay, how necessary the knowledge of her is, since there is no other means of entering into life unless she conceive us in the womb and give us birth, unless she nourish us at her breasts, and, in short, keep us under her charge and government, until, divested of mortal flesh, we become like the angels (Matthew 22:30). For our weakness does not permit us to leave the school until we have spent our whole lives as scholars. Moreover, beyond the pale of the Church no forgiveness of sins, no salvation, can be hoped for, as Isaiah and Joel testify (Isaiah 37:32; Joel 2:32). To their testimony Ezekiel subscribes, when he declares, “They shall not be in the assembly of my people, neither shall they be written in the writing of the house of Israel” (Ezekiel 13:9); as, on the other hand, those who turn to the cultivation of true piety are said to inscribe their names among the citizens of Jerusalem. For which reason it is said in the psalm, “Remember me, O Lord, with the favour that thou bearest unto thy people: O visit me with thy salvation; that I may see the good of thy chosen, that I may rejoice in the gladness of thy nation, that I may glory with thine inheritance” (Psalm 106:4, 5). By these words the paternal favour of God and the special evidence of spiritual life are confined to his peculiar people, and hence the abandonment of the Church is always fatal.
John Calvin, The Institutes of the Christian Religion (Ford Lewis Battles, trans., John T. McNeill, ed. Louisville, KY: Westminster John Knox Press, 1960), Book IV, p. 6.