If I may be permitted to weigh in here: Dr. Sungenis is right.
Pope Benedict XVI, even when lifting the 1988 excommunications on the SSPX bishops in 2009, said (via the Prefect of the Congregation for Bishops), that the Society was not "in full communion" with the Catholic Church, and that he hoped this gesture would be a step towards bringing them back into full communion.
As is well known, "not in full communion" with the Catholic Church is just the polite, ecumenically-oriented post-Vatican II term for being in schism and/or heresy. Protestant and Eastern Orthodox communities are also said to be "not in full communion" with the Catholic Church. (Lifting a canonical sanction such as excommunication does not in itself put an end to schism. Remember that after Vatican II, Pope Paul VI and the Eastern Orthodox Patriarch Athenagoras famously lifted the mutual excommunications imposed by their predecessors nine centuries earlier. But that doesn't mean the Orthodox are no longer in schism.)
Pope Francis, too, used the same expression (via Cardinal Mueller, head of the Ecclesia Dei Commission) in allowing bishops to validate marriages witnessed by Society clergy. The relevant letter of 3/27/2017 to the bishops begins, "As you are aware, for some time various meetings and other initiatives have been ongoing in order to bring the Society of St. Pius X into full communion." A few months earlier, in his Apostolic Letter Misercordia et Misera (11/20/2016), Francis had extended the validation of Confessions heard by SSPX priests and bishops that he had granted for the Jubilee 'Year of Mercy', saying, "For the pastoral benefit of these faithful, and trusting in the good will of their priests to strive with God’s help for the recovery of full communion in the Catholic Church, I have personally decided to extend this faculty beyond the Jubilee Year, until further provisions are made" (bold type added in thee quotations).
In short, none of the last three popes has ever revoked Pope St. John Paul II's determination that the SSPX clergy, and those laity who "formally adhere" to them, are in schism. The next two popes after him reaffirmed that determination, but did so in gentler language because they were making gestures designed to facilitate the return of the Society to "submission to the Roman Pontiff and communion with the members of the Church who are subject to him" (cf. definition of schism in the Catechism of the Catholic Church, no. 2089, citing canon 751 of the Code of Canon Law).
Unfortunately, the SSPX clergy promptly showed their continuing lack of submission to the Roman Pontiff by assuring their adherents that these two generous concessions by Pope Francis made no substantial difference whatever, because (they claimed) their marriages and confessions had always been valid anyway! Clergy who: (a) say they don't need permission from the Pope or the local diocesan bishop in order to publicly offer the full and valid range of pastoral and sacramental services (including even their own marriage tribunals); (b) operate for all practical purposes in complete independence from the aforesaid lawful Church authorities; and (c) forbid their adherents to attend 95% of all Catholic Masses (i.e., Novus Ordo's, which they condemn as 'non-Catholic' rites), and much less receive Novus Ordo Holy Communion - such clergy can scarcely be said to be "in submission" to the Roman Pontiff and "in communion with the members of the Church who are subject to him". Mere fig-leaves like mentioning the Pope's and the local bishop's name in the Canon of the Mass, and making occasional gestures like pilgrimages to Rome in Holy Years, are quite insufficient to cover up the schismatic condition of the SSPX.
Indeed, it appears the SSPX are in heresy as well as schism. Canon 7 of the Council of Trent's Session XXIII on the Sacrament of Order declares an "anathema" against anyone who says that "those [clergy] who have been neither rightly ordained nor sent by ecclesiastical and canonical authority (qui nec ecclesiastica et canonica potestate rite ordinati nec missi sunt), but come from a different source, are legitimate ministers of the word and sacraments" (Dz 967 = DS 1777). Well, the SSPX clergy cannot and do not claim that they have been either ordained or sent by "the ecclesiastical and canonical authority" - that is, by the pope and the local diocesan bishop. They freely admit the historical fact that they come "from a different source", namely, from Archbishop Lefebvre, who consecrated their present bishops in an act of direct disobedience to the Roman Pontiff. And yet all these clergy claim to be "legitimate ministers of the word and sacraments".
It is clear from the other errors condemned in this same canon 7 that this a doctrinal 'anathema', not a merely disciplinary one that could be changed by some future pope or council. There is clearly no way the Church could ever say that priests and bishops with no authority from either the pope or the local Ordinary can just come into a diocese and start ministering 'off their own bat', condemning the approved Masses in that diocese and pulling people away from attendance at them. That would go completely against the unity of the Church.
Fr. Brian Harrison, OS, MA, STD