The Church doesn’t “throw people out”.
But even if that were the case, things are healed now almost to the point of “full communion” (whatever that term means…). The Church has granted faculties to the SSPX to celebrate all seven sacraments, and the Church does not grant faculties to entities that are not in union with her, and that are not under her jurisdiction. Archbishop Lefebvre has gone on to his eternal reward and can no longer be “reunited” to the Church. His lieutenants can and have been (Bishop Williamson is another story).
A partially applicable secular analogy might be Taiwan
as seen from the standpoint of the People’s Republic of China — part of the PRC, theoretically subject to the PRC, not a separate country, if Taiwan ever declared independence, it would be a
casus belli, but they’re not going to do that. As a practical matter they “do their own thing”, nobody (except they themselves) takes seriously their claim to be the true government of all China, and somehow, everyone on both sides “muddles through” the situation and things about halfway work the way they should —both sides occasionally bare their swords and gnash their teeth, but that’s only to be expected, it doesn’t mean they’re about to go to war. Taiwan has business interests in the PRC and Taiwanese travel freely to the PRC and back again.
Again, an imperfect analogy, not so much “apples and oranges” as “oranges and tangerines”, but an example of how two adversaries can work together, and at least in theory, act as though they are one entity — even if the two sides disagree on the ideal structure of that entity and what that means.