The 2 items in question "public abjuration" and "public retraction" .... these are not a public confession, which is what your quote is referencing.  Your quote has nothing to do with abjuration/retraction.

An abjuration/retraction is a formal admitting that you were a heretic/schismatic.  That you believed, supported, condoned, and pushed error.  Since your errors were public, then your retraction must be public.  It's exactly the type of letter that +Vigano wrote.  He admitted he was wrong about V2, and Conciliarism, the new mass, etc.  Then he explained why they are wrong and Orthodoxy is right.
All Trent is saying above is that it's not a Divine requirement.  It also says that SECRET sins should not be made public.  But sins of heresy/schism are NOT SECRET.  They cause scandal and the scandal must be undone.  So says canon law.  That's the whole point of a suspected heretic being "called to rome" to be interrogated.  It's the entire basis of the Spanish Inquisition.  Suspected heretics were examined to determine if they were a) confused on doctrine (material heretics, or b) obstinate in error (formal heretics).

  No one is talking about in 'danger of death' which situation has all manner of exceptions.

As I said Pax, stop making your own rules. Per canon law (you can look it up) normally, confession is all that is necessary - unless the confessor or bishop require a public abjuration, or, if the penitent is a new convert. 

No, it’s wrong in all senses. A heretic is not a Catholic.

Try to define heretic without using the word 'catholic'.

As I said Pax, stop making your own rules. 

I'm not.  I'm pointing out the different levels of crimes in canon law.  You are simply generalizing the crimes. 

Per canon law (you can look it up) normally, confession is all that is necessary

See?  You're using the word "normally" which is the general rule.  But this means that there are cases where confession IS NOT ALL THAT IS NECESSARY.  There's more required in order to obtain forgiveness.

Martin Luther could not simply go to confession and act like the 99 thesis he nailed to the church door didn't happen.  He was summoned to a meeting to be interrogated for his heresies, as his crimes were extreme.

 - unless the confessor or bishop require a public abjuration, or, if the penitent is a new convert. 

Or if the penalty requires a special forgiveness from the roman official, or a roman judge, or the pope himself.

Again, there is the general rule (which you hyper-focus on) and you are forgetting all the exceptions and other special cases which are contrary to the general rule.

You do this all the time.  Admit that the general rule AND exceptions exist.  You can't pick and choose.  It's both.

I'm not.  I'm pointing out the different levels of crimes in canon law.  You are simply generalizing the crimes. 
See?  You're using the word "normally" which is the general rule.  But this means that there are cases where confession IS NOT ALL THAT IS NECESSARY.  There's more required in order to obtain forgiveness.

Yes, *normally* = confession is all that is necessary, and confession is as necessary for the sin of heresy to be forgiven as it is for all mortal sins.

If there is a censure connected with the particular sin of heresy - which would have to have been pronounced to the individuals by the pope or bishop - not any laymen, or if the confessor or bishop judges that the sin requires a public abjuration, then so be it, but that is not normally the case, what that is is a rare or an extraordinary case. Either way, only trad clergy/hierarchy are the ones who are found guilty of sins of that nature these last 60 years. 

If the pope deemed it appropriate for whatever reason, Luther could have received absolution without any abjuration at all. Public abjuration is NOT part of the sacrament.

But there are some things we lay people have zero say in - and insisting heretics MUST publicly abjure their heresy in order for the sin to be forgiven is one of those things. 

Yes, *normally* = confession is all that is necessary, and confession is as necessary for the sin of heresy to be forgiven as it is for all mortal sins.

Thank you, captain obvious.

Here's the problem, you are hyper-focused on the forgiveness of the sin (i.e. which only happens through confession...no one is arguing otherwise).  What you are minimizing is the ADDITIONAL penalties which heresy/schism causes, due to canon law.

If there is a censure connected with the particular sin of heresy

YES!!!  This is what we're talking about.  The grave, serious and extreme cases of heresy/schism which canon law IPSO FACTO imposes on such sins.

- which would have to have been pronounced to the individuals by the pope or bishop - not any laymen,

many of these censures are automatic, as canon law clearly states.  That's what IPSO FACTO means.  "By the fact" that (person A did x, this is the penalty).

or if the confessor or bishop judges that the sin requires a public abjuration, then so be it, but that is not normally the case,

  But we're NOT talking about normal cases. 

what that is is a rare or an extraordinary case.

Yes.  And Martin Luther is a rare case of extreme heresy.  Just like most of the V2 heretics.

If the pope deemed it appropriate for whatever reason, Luther could have received absolution without any abjuration at all.

The point being, the pope has to decide either way.  Confession alone does not suffice.

Public abjuration is NOT part of the sacrament.

No one ever said it was.  You're not distinguishing between the CANON LAW penalties of excommunication and the power of confession to forgive sins.

Christ gave the Church the power to bind and loose.  Certain sins (i.e. heresy/schism) have been BOUND by the Church to a greater degree, and require MORE than just confession.  The acts are BOTH sins and also violations of Church law.

If a person is excommunicated in the most extreme degree, they can go to confession and be forgiven, but... they are still not allowed to go to Communion and take part in public worship.  The excommunication is related to the heresy/error of dogma.  The confession is related to the sin.

Again, looking at Martin Luther, he originally started with 99 heresies.  After being summoned to an inquiry, he was corrected and recanted 40 of these.  But he was obstinate in heresy, after being corrected, on the rest.

This whole process, inquiry, investigation took multiple years.  All the while, he was excommunicated....which means, he was not allowed to take part in public worship.  He was on probation, so to speak.  Even if he had gone to confession every single day of this multi-year period.

His excommunication meant he was not a "member in good standing" of the Church.  Again, he was on probation.  Until the Church decided on whether he was obstinate in his heresies or not.

Confession does NOT solve every problem.  That's the whole point.  And Christ gave His Church the power to investigate, inquire and determine serious cases.

But there are some things we lay people have zero say in - and insisting heretics MUST publicly abjure their heresy in order for the sin to be forgiven is one of those things.

We're insisting on following canon law.  No one is arguing for penalties which don't already exist in canon law.

Do you honestly believe that this "abjuration of heresy" is not part of canon law?

Here's another thing, which you fail to consider:
1.  A firm purpose of amendment is required for forgiveness.  An abjuration of heresy is simply a firm purpose of amendment not to follow error anymore.
2.  A public heretic can be forgiven his sins in confession.
3.  An abjuration of heresy is simply their PUBLIC denial of errors, based on their PUBLIC sins, which is an extension of their firm purpose to reject heresy from now on.

Again, +Vigano's letter was an abjuration of heresy, of sorts.  So was St Augustine's "Confessions".

The Church can require EXTRA things (apart from confession) to be forgiven, just like a priest can require a thief to return property, or a murderer to turn himself in, or a perjurer to recant his lies in court.  So the Church can require a abjuration of heresy.

This is NOT some new concept.  It's part of Church History.

You can’t be serious?  Do you think Martin Luther was a normal case of heresy?

You can’t be serious?  Do you think Martin Luther was a normal case of heresy?

No. Luther, Henry VIII et all are not normal cases.

If you would have read the thread, you would see I tried to get QV and 2V to imagine themselves as heretics wanting to repent. = Normal.

 I did say at one point that a heretic could be Luther and Calvin combined and still be absolved in confession, but I meant their heresies, not their notoriety.