It seems hardly respectful, with regard to a body as admirable as the SSPX, for an outsider to discuss its 'status'. I write what follows aware that it may seem arrogant to the point of being infuriating; and with very real apologies to readers who find that I am simply making them angry.
The status of the SSPX has, in my reading, always or usually been treated in canonical terms. Thus, 'states of necessity' become points of discussion. I cannot help wondering whether it might be more realistic to discuss it in terms of Ecclesiology.
In the CDF document Communionis notio of 1992, there is a chapter "De Communione Ecclesiali et OEcumenismo". It affirms the existence of a "Communio quaedam etsi non perfecta" with separated Christians. It then goes on to discuss the status of "Ecclesiae orientales orthodoxae", explaining that, although seiunctae a Sede Petri, they "cum Ecclesia Catholica coniunctae esse pergunt".
The reason for this is that they possess "successio apostolica et valida Eucharistia", and, because of this, deserve (merentur) the 'titulus Ecclesiarum particularium'. Quoting Vatican II, the CDF assures us that "per celebrationem Eucharistiae Domini in his singulis Ecclesiis, Ecclesia Dei aedificatur et crescit"; and then adds to the conciliar wording this interesting and thought-provoking phrase "quia in quacumque valida Eucharistiae celebratione vero praesens fit Ecclesia una, sancta, catholica, et apostolica."
I am not suggesting a precise identity between Separated Byzantines, and the SSPX. But the principles which apply in the favour of one can hardly be denied to the other.
The defences often advanced for the position of the SSPX state or imply that it is has the same status as organisations such as, for example, Opus Dei or the Dominican Order. It seems to me that, given the decades which have followed the Econne consecrations,this description no longer ticks the necessary boxes. Indeed, at a human level, one might wonder whether it is appropriate for Roman Pontiffs to fawn upon Separated Byzantines (and even Separated non-Chalcedonians), sometimes (literally!!!) grovelling before them, while maintaining a disdainful distance from a community which is theologically closer to the full Magisterium of the Catholic Church than are the Separated 'Orientals'.
The curious action of PF in not granting formal faculties to absolve to SSPX clergy, while 'giving permission' to the laity to go to them for Confession, seems to me to express perfectly (if unintentionally!) the ecclesiological analysis which, I argue, is offered by Communionis notio.
How 'ecclesial' is the SSPX? I suggest that one litmus-paper here might reside in the Chrism Mass and the use of the Oils of Chrism and of the Catechumens.
If a bishop ... say, Bishop Fellay ... makes available to a presbyter the oils which he has consecrated, and if that presbyter receives and uses them, then the Episcopal Ministry of that bishop becomes most intimately internal to all the rites of Christian Initiation performed by that presbyter.
This, it seems to me, is ecclesial and sacramental.