Can anyone answer this in brief?
I thought that the SSPX was excommunicated due to them rejecting some teachings of Vatican II and finding Popes Benedict and John Paul II to be invalid Popes. Why were they excommunicated then?
Only their bishops, for the ordination of 4 bishops in direct rejection of orders not to from the Pope.
The invalidity issues are a heresy, sedevaticanism, and whilst common amongst lay adherents to the SSPX, not really part of the SSPX platform. The SSPV, however… but they are a different bunch of schismatics.
One MUST divorce what the lay-followers of the SSPX hold from what the SSPX itself teaches. The SSPX is a society of secular priests and deacons; they cound in their number seminarians and subdeacons, tho current canon law does not count those men as clerics.
The SSPX at present holds that the OF mass is valid but inappropriate and
maybe even illicit; many of the followers believe it to be invalid and damnable. The SSPX holds that the pope is still their pope, but that their disobedience and continuing disobedience was & is justified; a small fraction of the lay-followers hold that there has been no pope since Pp. Paul VI; A smallter still group reject Popes John XXIII & Paul VI as well. The SSPX considers subdeacons major orders; the church as a whole ceased to do so at Vatican II, since the order of Subdeacons is not biblical in origin (while Priests, Deacons and Bishops are), and in fact abolished the order for the Roman church. The SSPX has never attacked the Eastern Churches in Union with Rome; many lay adherents of the SSPX do so regularly, either claiming them a heresy or by attempting to push for latinzations.
The only problems with the SSPX are that it has usurped the role of an autonomous church (A church Sui Iuris), and that it rejects the authority of Rome over itself. The problems of many of the SSPX’s lay-adherents is that they go well beyond anything the SSPX itself permits, and that many of them reject Rome’s authority over the SSPX.
And then there’s Bishop Williamson… who has chosen to take some very unhealthy views and make them very public.
As a generality, however, the SSPX itself rejects Rome’s authority, whilst asserting Rome’s primacy, and keeps the catholic faith,