The following is from Jonathan Edwards’s Treatise on Qualifications for Full Communion.
It is evident that God sometimes, according to the methods of his marvelous mercy, and long suffering towards mankind, has a merciful respect to a degenerate church, that is become exceeding corrupt in regard that it is constituted of members who have not those qualifications which ought to be insisted on. God continues still to have respect to them so far as not utterly to forsake them, or wholly to deny his confirmation of, and blessing on their administrations. And not being utterly renounced of God, their administrations are to be looked upon as in some respect valid, and the society as in some sort a people or church of God. Which was the case with the church of Rome, at least til the Reformation and Council of Trent; for til then we must owe their baptisms and ordinations to be valid.