St. Alphonsus calls the opinion contrary to Jone's (the claim it is a mortal sin) the common and "verius" ("more true") opinion, in Theologia Moralis lib. 2 n. 916.
The argument is simple: just as inchoate fornication is still fornication, inchoate sodomy is still sodomy.

Yes, it was the common opinion TWO HUNDRED YEARS before Jone.  That had changed by the time his book was written.

Since I have not studied this in detail, I cannot give a definitive answer on the matter.  I would go by whatever the theology manuals held regarding the practice of NFP without grave reason.  If the penitent cited such a text legitimately, then I would defer to it.  Now, my gut feeling is that the indiscriminate use of NFP with no other reason than convenience would be a grave sin, since one would be deliberately attempting to frustrate the primary end of marriage.  There are probably other factors involved.  If someone did this for two to three months, it might be venial (vs. doing it for 10 years straight).  If someone had a reason that was borderline grave and might rise to the level of justifying it, that might also be venial.  Again, hard to say, since I have not studied the question in depth.  So just speculating here.

Grave reason is a bit tough, as it might be arguable.  Also, the confessor would have to sift through whether the penitent was exaggerating some difficulty in order to rationalize the practice which was really being engaged in for convenience.  People have a tendency to "find" reasons to justify their actions.  "Oh, our doctor told us that the mother's life was at stake."  That too the physicians tend to exaggerate in order to protect themselves from possible malpractice claims.  So there's a lot to wade through with this.

OK, I guess the core of my question is, a person who isn’t a committed trad attends your chapel for whatever reason (say it’s an sspx chapel and thus Rome says they can, or something) and the penitent cites a post Vatican ii source to you to justify their actions, would that be good enough assuming it was cited correctly for you to commune them or not 

I think I'm missing something here.  If the hypothetical penitent thinks his actions are justified, how/why would he be confessing it in the first place?

I think ladislaus meant would you deny absolution for a DIFFERENT sin because of the use of NFP 

I think ladislaus meant would you deny absolution for a DIFFERENT sin because of the use of NFP

Right ... absolution in general.

OK, I guess the core of my question is, a person who isn’t a committed trad attends your chapel for whatever reason (say it’s an sspx chapel and thus Rome says they can, or something) and the penitent cites a post Vatican ii source to you to justify their actions, would that be good enough assuming it was cited correctly for you to commune them or not

In the Novus Ordo, the entire system has broken down.  Very few self-styled theologians these days would even come close to qualifying as such prior to Vatican II, and yet every other one feels entitled to publish his own ramblings and reflections far and wide.  So there would have to be appeal to some formal Church teaching rather that to some Novus Ordo pamphlet or the ramblings of some Modernist priest.  Appeal to Novus Ordo sources is probably the equivalent to appealing to, say, my posts here on CathInfo.  Now, if there were appeal to some specific putative papal teaching, then that might be more difficult.  If the person is convinced that Paul VI was a Pope and appealed to something in Humanae Vitae and considered it to be Church teaching, I could see a person having a sincerely informed conscience ... although that too could be just rationalization.  Thankfully, Wojtyla did keep most Catholic MORAL teaching intact ... although Bergoglio has begun to undermine it, especially with Amoris Laetitia.  I would not accept an appeal to Amoris Laetitia as legitimate justification for cohabitation.  Even Amoris Laetitia gives most of the discretion to the priest, and as a priest I would deny such appeals.  In fact, Bergoglio directly contradicts Wojtyla on this matter in Amoris Laetitia, so an appeal to the latter entails a rejection of the former.

This crisis is so very sticky in many ways, since, even though the Conciliar establishment really entails the establishment of a religion (doctrine and worship) that is alien to the Traditional Catholic religion, most still consider themselves to be Catholic, profess the true faith, and are only in material error.

That's not how BysCat's hypothetical situation sounded, but I understand what you are saying.

I may have worded it badly, but ladislaus got the intent of it