Schism is a rupture of unity in the Church. When many think of schism, they think of the consecration of four bishops by Archbishop Lefebvre on June 30, 1988, done against the wishes of Rome.
In 1988, the SSPX said there was no schism because the new bishops had no jurisdiction. Today, these bishops of the SSPX now claim to have jurisdiction, because they grant marriage annulments and impose censures on laypeople, and this requires jurisdiction.
How could we know that the SSPX is now in schism due to the jurisdiction they have taken for themselves? It's not by asking Rome who opposed the consecrations of 1988, or by asking the SSPX. No-one will ever admit that they are in schism. So, how could we know? Fortunately, there are books on canon law and schism which we can study to know whether the SSPX is in schism or not, based on the principle that if someone illegally takes on the jurisdiction belonging to the Pope, then they are in schism – it doesn't matter what the SSPX says otherwise.
Again, I am not associated with the SSPX in any way. Indeed, I actually attend an FSSP parish (if anyone throws tomatoes, I will make a nice salad). However, I have friends who have or currently attend SSPX chapels. I also have sympathy with them and listen to SSPX sermons from the Internet regularly just as I listen to FSSP sermons. If I had to choose between the NO and the SSPX, I would go SSPX. ABL is one of my "heroes" on my Facebook page and I do believe that they work they are doing is very important and necessary. When Russia is consecrated to the Immaculate Heart and Catholic Tradition is restored in the Church, I am certain ABL will be rehabilitated and canonized.
That being said, you should be aware of the SSPX's defense of the Canonical Commission, through which they have made declarations of nullity regarding marriage. One of the chief issues regarding marriage annulments is to understand what an annulment is. An annulment is a finding of fact, it does not change anything that exists. A true (ratified and consummated) Sacramental (by two baptized persons) marriage cannot be dissolved by any power on earth, except death. But not all putative marriages are true marriages. This is where annulments come in. An ecclesiastical court may rule that there was some defect at the time of the wedding which rendered the marriage invalid (such as a Catholic being married by a Protestant minister or judge, without dispensation).
The annulment crisis in the United States (and, to a lesser extent, other countries but especially the US) means that many annulments which are "granted" are invalid and a couple who knows that their annulment is bad because of a defect in the evidence (i.e. they lied) or a defect in the decision-making skills of the court (superfluous reasonings, which are common) sins mortally if they attempt marriage with someone else. (Obviously, if a couple honestly thinks the court decision was valid, they do not commit a sin but new marriages are, of course, still invalid). The purpose of the Canonical Commission is to circumvent this problem and make better decisions regarding marriage annulments. It does not claim ordinary jurisdiction and thus it does not claim to have the full force of law, it is only a practical decision since the Tribunals of the Conciliar Church are so bad that they cannot be trusted to make an accurate assessment of the situation. Thus, the Canonical Commission is better than nothing.The SSPX & Annulments