Faith is what we do. We can do some things wrongly or do them out of a false conviction, but nevertheless that is what faith is. The desire to distill some purely intellectual content and call that faith, and the rest “works” is not found anywhere in the Gospel. It is a New Times invention.
Now, that doesn’t make things magical. It is God’s choosing to make baptismal water salvific or make blood into wine. It sure is supernatural, as is the subject matter of all Christianity.
You point out validly that the historical apostolic faith is integral with the liturgical and charitable works that embody it. Protestant faith, in contrast, if like Jefferson’s Gospel, a faith on its way out to be snuffed completely.
Of course it is possible for a non-Christian to have a sincere prayer to God Whose name he does not know and Whose Church he never stepped into. Since we are saved by our works and not by faith alone, it is possible for non-Christians to be saved, too. This should not be surprising to you, given, for exampe, the parable of the Talents. That righteous non-Christian was given so little, yet he may produce a far better yield, and the grace of Our Lord Jesus Christ be on him, — rather than on an emaciated, untested, declarative faith of a middle class American, who then has the gall to declare himself not only with faith, but already “saved”.
Wait a minute! :) We say that works flow from true faith and are evidence of it. We believe in perseverance of the saints. IOW, in essence faith and works are two sides of the same coin. Without true faith there are no true works, and (under normal circumstances) one either has and does both or neither. So, we do not have the sense of separation that I interpret you describing above. Indeed, it is the Catholic side which seems to split faith and works into two separate categories. It is Catholics who allow for the general possibility of true faith without works (and even vice-versa), not the Reformed. So, if I'm following you I agree that this treatment is found no where in the Gospel. :)