I know a fair number of SSPX people, and it’s interesting to discuss the Church with them. They absolutely are not sedevacantist, and, at least in our discussions, there is no disagreement in doctrine between their beliefs and mine; at least that I have heard. It’s more “around the edges”. Their approach to ecumenism, basically, is that they want no part of it, for instance.
Their orders are valid, and there’s no way around that. LeFevre might have been a crank, but he was a real bishop. Therefore, their sacraments are also valid since their priests are really priests and they are most punctilious about following the prescribed form of the sacraments (more so than some NO priests are).
They do object to the use of the vernacular at Mass, and that seems to be pervasive. But I have never heard one say that N.O. Masses are frankly invalid, though they do think some of the highly innovative Masses likely are. They do not hold themselves subject to the local bishops, but then, the local bishops don’t have anything to do with them, either. One does need to remember that the Tridentine Mass virtually disappeared in the U.S. and Europe after Vatican II; correction of which has had a start. Had it been more acceptable back in LeFevre’s time, they might not even exist now. Let’s be honest about it. VII did not forbid the Tridentine Mass. In fact, it encouraged its preservation. But a lot of bishops defied that and wouldn’t allow it, no matter what. My own former bishop was that way. He said he would never allow it within this diocese and for 25 years, he kept his word on that. He retired, and our new bishop actively promotes it.
And now, the Church is ready to accept an “Anglican Rite” different from the N.O. It has always accepted Byzantine and other rites; which also have their own bishops who are not subject to the Latin bishops or diocesan structures.
The SSPX are just out on a limb, you might say. They are not quite schismatic, but not quite unified with the Church either. They’re certainly much closer to being in union with Rome than are the Eastern Orthodox or the Oriental Orthodox, whose orders and sacraments we also consider valid.
One thing possibly worth mentioning. There are not a whole lot of them, but they do have a strong “community sense”. There are some places where they are so numerous as to perhaps be in the majority, locally. I understand, for example, that in and around St. Mary’s Kansas there are thousands of them. They have their own (excellent) Catholic grade schools and high schools and even a Catholic college there. Virtually all of their children attend those schools. They do have a lot of children per family and a lot of vocations. Kind of hard to be too harsh about them.
Personally, I am a bit queasy about the SSPX, but I don’t think its existence is a disaster, at least not yet. And it could end up being “regularized” in some manner, particularly since it seems so many of the newer bishops in the Church in the U.S. seem more faithful to the magesterium and less oddly “innovative” than was formerly the case. After all, if you were a priest ordained by an SSPX bishop, would you have welcomed the thought of being subjected to the former Cdl Mahoney? But that all might change, and if it does, I personally think they will be a positive addition to the “regular” Church in the U.S.