The only kind of dialogue I think we can have with them, under the circumstances, is ecumenical dialogue, such as the Holy See has with other non-Catholic ecclesial communities.
The SSPX is being handled by the Congregation for the Doctrine of the Faith. If it were only a liturgical issue, and not doctrinal/dogmatic in nature, a liturgical commission or congregation would be taking care of business. That is simply not the case. As the Holy Father himself stated in Ecclesiae unitatem
, there are doctrinal issues separating Rome and the SSPX. Doctrinal, and not simply liturgical. It is clear that no bishop or priest of the SSPX yet enjoys valid faculties anywhere in the Catholic Church.
However it is clear that the doctrinal questions remain, and until they are clarified the Society has no canonical status in the Church, and its ministers cannot legitimately exercise any ministry in the Church.
"Cannot legitimately exercise any ministry in the Church" is far more onerous in its extent to clergy other than the four bishops than Ecclesia Dei
, which only dealt specifically with the four bishops in the ipso facto
excommunication. The current document extends to all clergy in the SSPX, "its ministers".