If the allegedly 'inspired' person's teachings contradict the doctrine of the Church, then they are not of God.
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NO. IF the supposedly inspired person's teachings contradict what God is saying and doing in that situation at that time . . . and/or with Scripture . . . then things are at best exceedingly suspect if not well over the line and likely from hell.
As determined by whom? Heretics? Obviously not, otherwise, every heresy of every sort would have claim to "divine inspiration". Orthodoxy is determined by the bishops of the Church; that is precisely what distinguishes orthodoxy from heterdoxy. Orthodoxy is not determined by agreement with one's own private and personal interpretation of Scripture or one's own private and personal determination of "what God is saying". That would entail the elimination of orthodoxy (and heresy) altogether, for then each person would have his own orthodoxy, evacuating the very concept of all meaning.
That is why St. Augustine is exactly right when he says: "For my part, I should not believe the Gospel except as moved by the authority of the Catholic Church." Notice the contrast between the great saint Augustine, and the contemporary individualist for whom the Church has nothing to do with the Gospel or salvation; it just "me and Jesus". In actuality, it is not the Bible per se that determines orthdoxy (as 20,000+ different 'sola scriptura' sects demonstrate); it is fundamentally the Church, particularly, her bishops in succession from the Apostles and in communion with the bishop holding the seat of Peter. Just as in the days of the Apostles, to enter the Church was to enter into communion with the Apostles and to submit to their leadership and authority, so today to enter the Church is to enter into communion with those bishops in succession from the Apostles and submit to their leadership and authority.
-A8