In the older prayer books, there was an exhortation to the very effect of the OP. Likewise, the rubrics called for the minister to publicly admonish anyone who was known to be living in a state of lawlessness not to come to the altar until they had repented. In my recent experience, the exhortation is read only once a year, prior to Lent. As for calling out the reprobates in the congregation, I have never seen it happen. Of course, with recent news and events, one might wonder if some Anglican churches still identify anyone as reprobate.
The exhortation:
DEARLY beloved in the Lord, ye who mind to come to the holy Communion of the Body and Blood of our Saviour Christ, must consider how Saint Paul exhorteth all persons diligently to try and examine themselves, before they presume to eat of that Bread, and drink of that Cup. For as the benefit is great, if with a true penitent heart and lively faith we receive that holy Sacrament ; so is the danger great, if we receive the same unworthily. Judge therefore your-selves, brethren, that ye be not judged of the Lord ; repent ye truly for your sins past ; have a lively and steadfast faith in Christ our Saviour ; amend your lives, and be in perfect charity with all men ; so shall ye be meet partakers of those holy mysteries. And above all things ye must give most humble and hearty thanks to God, the Father, the Son, and the Holy Ghost, for the redemption of the world by the death and passion of our Saviour Christ, both God and man ; who did humble himself, even to the death upon the Cross, for us, miserable sinners, who lay in darkness and the shadow of death ; that he might make us the children of God, and exalt us to everlasting life. And to the end that we should always remember the exceeding great love of our Master, and only Saviour, Jesus Christ, thus dying for us, and the innumerable benefits which by his precious blood-shedding he hath obtained for us ; he hath instituted and ordained holy mysteries, as pledges of his love, and for a continual remembrance of his death, to our great and endless comfort. To him therefore, with the Father and the Holy Ghost, let us give (as we are most bounden) continual thanks ; submitting ourselves wholly to his holy will and pleasure, and studying to serve him in true holi- ness and righteousness all the days of our life. Amen.
And this, the call to the general confession, which I think of as a short form of the exhortation:
YE who do truly and earnestly repent you of your sins, and are in love and charity with your neighbours, and intend to lead a new life, following the commandments of God, and walking from henceforth in his holy ways ; draw near with faith, and take this holy Sacrament to your comfort ; and make your humble confession to Almighty God, devoutly kneeling.
The rubrics:
¶ If among those who come to be partakers of the Holy Communion, the Minister shall know any to be an open and notorious evil liver, or to have done any wrong to his neighbours by word or deed, so that the Congregation be hereby offended ; he shall advertise him, that he presume not to come to the Lord’s Table, until he have openly declared himself to have truly repented and amended his former evil life, that the Congregation may thereby be satisfied ; and that he hath recompensed the parties to whom he hath done wrong ; or at least declare himself to be in full purpose so to do, as soon as he conveniently may.
¶ The same order shall the Minister use with those, betwixt whom be perceiveth malice and hatred to reign ; not suffering them to be partakers of the Lord’s Table, until he know them to be reconciled. And if one of the parties, so at variance, be content to forgive from the bottom of his heart all that the other hath trespassed against him, and to make amends for that wherein he himself hath offended ; and the other party will not be persuaded to a godly unity, but remain still in his forwardness and malice ; the Minister in that case ought to admit the penitent person to the Holy Communion, and not him that is obstinate. Provided, that every Minister so repelling any, as is herein specified, shall be obliged to give an account of the same to the Ordinary, within fourteen days after, at the farthest.