As Bishop Tissier wrote, there are two aspects of a society, its members, and its aims. There are certainly people who are materially part of the Conciliar Church (simply because they perceive it to be the hierarchy) but not because they formally endorse its errors. These are those who apply the "hermeneutic of continuity" and try to establish a continuity, but otherwise are not Modernists ... except to any extent that they have been subtly influenced by it almost without even being aware of it.
In that sense, while they are materially part of the Conciliar Church, they formally belong to the Catholic Church.
But it is the POPE that determines the aims of that society, and so he can't be merely materially part of the Conciliar Church. That's where this totally breaks down. What applies to the members of the society cannot apply to the head. These guys are setting the agenda and driving the aims of that Conciliar Church, so to claim that they are just somehow along for the ride as being in material error is utterly absurd. They are the ones who CREATED the very aims of this counter-Church, this counter-society. They brought it into being and keep it alive.