Manifest heretics can't simply be absolved in Confession.  That's only for occult heresy, say you consented to a heretical proposition in your mind.  Once you become a manifest heretic, you have to be received back into the Church, make an abjuration of error and profession of faith.

You're confusing the sin of heresy with the public/manifest heresy, which excludes from membership in the Church, according to St. Robert Bellarmine and every theologian in history bar one.

No, manifest heresy is a sin and like all sins can be absolved in confession. Where did you come up with "that's only for occult heresy?"

Did you miss (or simply ignore) this part of the quote?
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the prior abjuration being conducted juridically and observing those other things that in law ought to be observed; and one thus absolved can thereupon be absolved from sin by any confessor in the forum of conscience.

Once the person has been received back into the Church in the EXTERNAL forum, then he can be absolved "in the forum of conscience".

No, I did not miss that part, but you must have missed this part:

But if, however, the delict of apostasy, heresy, or schism has been brought in any manner to the external forum of the local Ordinary, even by voluntary confession, that same Ordinary, but not the Vicar General without a special mandate, can by his own ordinary power absolve one duly recovered in the external forum

Which means that as long as the penitent walks into the confessional and confesses his sins of apostasy, heresy or schism, the priest can absolve him from his sins just the same as every other member of the Church. 

Isn't the bishop the ordinary not the priest?

Not these days. Besides, him going to a NO bishop would pretty much defeat the whole purpose - no?

I don't follow you.  If the ordinary is the bishop how does going to a priest absolve from heresy?  You are saying since there are maybe a few ordinaries left and most places don't have one the rule is null and the priest can do it?

I'm saying these days, the Prior of a trad chapel *is* the Ordinary. If that is unacceptable or wrong, then like any other member of the Church, a heretic could also simply go to a NO Bishop for confession....which still and again, is a something only those inside of the Church can do - which is precisely the point. 

If those who've lost the faith and became heretics, Apostates and schismatics are outside of the Church and no longer members, then the sacrament of confession (and all the other sacraments) are as completely closed to heretics as they are to everyone else who is outside of the Church. But that's not the case with fallen away Catholics who've become repentant heretics, they still have the same privilege of being absolved in confession as all the other members- because even as a heretic, they are still a member.

Trent even teaches that in danger of death, it does not matter what your sin or censure is, even heretics wanting to repent can receive the last sacraments or must get to confession - even if that means receiving these sacraments from a heretic priest.

This is a major sticking point for sedes who, based on some theologians' speculations, insist heretics are not members, as such the pope cannot be pope because being a heretic he is not a member, and if he's not a member he is not pope. Next they claim these speculations are Divine Law, but have yet to say which Divine Law it is, also when or where this law has been revealed - and why a non-member can receive sacraments that only members are allowed to receive.

Father Hesse:

"... One of the reasons why we cannot positively state that this pope is not pope is because first of all we need proof. We do not have this proof. Some people quote the apostolic bull of Paul IV, cuм Ex Apostolatus against the present pope, saying that Paul IV decreed that a heretic cannot become pope. Yes, but the papal election is an act of administration, not a sacrament. It is not a theological procedure, therefore there cannot be an infallible pronouncement on it. It is an act of administration just like all elections. When in a monastery an abbot is elected, this is a canonical election. The election of the supreme pontiff among the cardinals is a canonical election. And those rules can not only be changed, but were changed a couple of dozen times over in Church history. Leo XIII changed the rules, Pius X changed the rules, Pius XI changed the rules again, Pius XII changed the rules again, Paul VI changed it, and the present pope changed it again. And none of them has ever quoted Paul IV again on this. Now the bull cuм Ex Apostolatus is an infallible bull as far as the doctrinal statements are concerned. It cannot be infallible as far as an administrative rule is concerned, saying that if a cardinal was a heretic, even if he was a heretic and converted, he cannot be validly elected pope. To be validly elected pope you need positive human law and law of administration, and that every single pope can change, much unlike the doctrinal laws, which no pope can change ever. If a pope decides on a moral issue, his successor cannot change it. Impossible. He would put himself in schism with the Church. But a rule of administration, and how it can be changed! And how! In the beginning the people of Rome elected the pope. Later on, it was the clergy of Rome, and very much later on, only 1300 years after Christ died and ressurected and founded His Church at Pentecost, cardinals were the only ones to elect the pope. So if a future pope says, "I don't want cardinals to elect the pope, but all of the bishops in the world," he's gonna make a mess but that doesn't make the election invalid. It would be horrible. I don't want to think of it. But it doesn't make the election, duly procedures required and provided, it doesn't make it invalid because it's an act of administration. And that's why I recommend the sedevacantists to be a little more careful with their judgements. The Society of Saint Pius X is not exactly composed of all idiots, and none of them nowadays consider the Apostolic See vacant. And the three priests, Fathers Sanborn, Kelly and Cekada unfortunately, because they are otherwise very good theologians, unfortunately had to be kicked out of the Society of Saint Pius X for insisting on the "fact" that we do not have a pope. To me this is a neurotic statement, too, because you put yourself in a dead end. Who's gonna elect the next pope? I leave the question to you."

Thank you NIFH for Fr. Hesse’s explanation.  I found it most helpful.