For the Society of St. Pius X (SSPX) to achieve full communion with the Church, there are multiple obstacles standing in the way that have nothing to do with doctrinal problems and everything to do with logistics.
The SSPX, as everyone knows, began its work from within the Church. After Abp. Marcel Lefebvre's illegal ordination of priests in 1976, followed by Lefebvre's suspension a divinis, the SSPX turned inwards. As the years dragged on and the Society grew, the SSPX was faced with various administrative problems. To remain outside the Church and continue functioning, it needed its own finances, schools, seminaries and chapels — which it managed to obtain. By the the time of this writing, one can accurately say the SSPX has set up a parallel church (the Church of the Priestly Fraternity of St. Pius X, as Pope St. John Paul II put it in his 1988 motu proprio Ecclesia Dei), complete with its own financial scheme and judicial proceedings.
The SSPX has roughly 600 priests and anywhere from 500,000 to a million people who assist at their Masses. The SSPX has built hundreds of chapels across more than 50 countries. They have six seminaries and are building a seventh. In the United States alone, the SSPX has a bishop, 85 priests, a college and 26 schools. Bear in mind that the United States makes up only about five percent of the total worldwide population that attends SSPX chapels.
Operating a trans-national organization on this scale is no easy task on a good day, and — should reunion ever come — integrating it into the overall financial network of the Vatican will be a nightmare. This isn't to say the SSPX is hoarding money or its bishops are involved in questionable financial conduct. We make no such accusation. But the finances backing the operation must be investigated when you are responsible for millions and millions of dollars of other people's money.
So far, in the talks between Rome and the SSPX, the popes have been quite generous. The SSPX has been offered a personal prelature directly under the authority and protection of the Pope, which removes the possibility of the Society's assets falling into the hands of hostile local bishops. At the same time, the Society would be surrendering final authority over their assets to the Holy Father, which requires a tremendous amount of trust — something the SSPX clearly lacks towards Rome.
The financial landscape would also be altered unpredictably. Donors not on board with a reconciliation will pull their funding, which may require the SSPX to sell off properties. Furthermore, many of the clergy may refuse to go along with the Society, break off from the group, and make off with its real estate. This has already happened multiple times before over various issues — the Society of Saint Pius V is one of many examples.
This isn't a question of being motivated by money. It's an administrative matter that any leader of such a large, financially well-off organization must consider.
It wouldn't be a stretch to say that reunification would cause a convulsion in the SSPX, as the prospect did several years ago, when approximately 60 SSPX clergy left its ranks over disagreements over potential reunion with Rome. The SSPX is unlikely to reach out to the local ordinaries for help, which will leave them in a bind. More than likely, if reunion were to occur, the SSPX would shrink. None of these are particularly welcome prospects for SSPX clergy pondering reunion.
Other organizations like the Priestly Fraternity of St. Peter (FSSP) have set up camp in various dioceses and operate independently (with the local bishop's approval). But the FSSP is nowhere near as large as the SSPX, which has an entire infrastructure operating parallel to the Catholic Church.
Questions abound. How would SSPX schools be integrated into the overarching Catholic school system? The SSPX is leery of almost all Church institutions, especially their catechesis, so they would need a special consideration in that matter as well.
Then comes the issue of marriage, perhaps the most significant hurdle to full communion from a logistical standpoint. The Society bears a deep distrust of the Church's marriage tribunals, so the SSPX has set up its own — a flagrant case of usurping jurisdiction. The Society has been issuing declarations of nullity, but those declarations carry no weight or legitimacy. Will the Church recognize their "annulments" and second marriages by laymen who have attempted marriage before SSPX clergy? Will all of those who have been processed by an SSPX tribunal have to re-submit their cases to actual marriage tribunals and start from stage one?
Since valid marriage requires jurisdiction, all SSPX marriages are invalid — or to put it in laymen's terms, those marriages don't actually exist. Unlike confession, where a penitent's sincerity can make an otherwise invalid confession valid (but still illegal and grave matter for the priest), there is no "common error" for marriage. A marriage conducted without jurisdiction simply never happens, no matter how sincere all parties are. (If this is your situation, there's a simple fix: Have your marriage convalidated by a priest/bishop who has legitimate faculties to do so.)
If the SSPX comes into full communion, those who have attempted marriage in the SSPX will have to come to terms with the fact that their unions have never been true marriages from the beginning, and all of them must be convalidated. That's a bitter pill to swallow — for the couples, and for the SSPX itself, which has to bite the bullet and admit it offered (perhaps unwittingly) false sacraments.
This isn't something the Vatican can just ignore. Those people have a right to be married, and the Holy See has an obligation to correct the injustice that has been done to them.
There's no doubt the SSPX operates as a parallel Church, in spite of its repeated denials to the contrary. The fact that it has functioned in this way for so long is a severe impediment to full union with Rome; the SSPX has operated independently for decades, is well-funded by generous donors, and has no shortage of supporters — why would it desire to be united to Rome which it distrusts, and believes it doesn't need? That is precisely the attitude we see among SSPX sympathizers today, and from the SSPX clergy itself, which responded with a half-hearted nod to the Pope's gracious gesture granting SSPX clergy the ability to absolve sins for the Jubilee Year of Mercy. The Society's response wrote off the Pope's concession as needless; after all, the Society claims to have supplied jurisdiction, and for them, that is enough.
Will these hurdles be overcome in the future? It is by no means impossible, and we pray for the SSPX's reconciliation daily. But it's clear setting up a parallel Church, while expedient, comes back to haunt every attempt to achieve reconciliation.