If a person becomes a heretic not just privately doubting a truth of faith, but an actual heretic. Or an Apostate which means denying Our Lord Jesus Christ.
He gets absolved secretly in the confessional. Then shows up at the Communion Rail. The faithful are rightly scandalized that this heretic is given Communion. The priest can say nothing. He cannot say I gave him absolution from his sin. The priest cannot explain because it is all secret and under the seal of the confessional.
He is outside the Church and must re-enter it in the same public way that any heretic or infidel enters it.
Negative.
The penitent's sins are forgiven in the sacrament of penance. This is the only thing necessary for the forgiveness of sins. Public abjuration is not part of the sacrament, never has been. One of the reasons those sins are the worst of mortal sins is because they are typically accompanied with so much obstinacy and wilful, vehement opposing of the true faith, that men who are guilty of it seldom or ever return to the faith, but this is due to their own obstinacy.
When we go to confession, no matter what our sin(s), even the above sins, the priest *first* removes whatever censure the Church may have attached to our sins, *then* he forgives the sin:
"....
May our Lord Jesus Christ absolve you: and I, by His authority, absolve you from every bond of excommunication, (suspension (for clerics)), and interdict, in so far as I am able and you are needful. Next, I absolve you from your sins, in the Name of the Father, and of the Son, and of the Holy Ghost. Amen."The forgiveness of those sins are given in the sacrament alone, which is something those outside of the Church have no access to, the remission of those sins is in no way dependent upon a public abjuration.