There is no such organisation as the "Conciliar Church". If Vatican 2 was a valid council, then the so-called "Conciliar Church" IS the Catholic Church. If the post-V2 Popes were valid, then their proclamations, decrees, promulgated rites, etc. were all done for the Catholic Church. It is ridiculous to assert that the Popes could've accidentally created a second Church that they didn't know existed and then accidentally only issued their decrees, etc. for the "Conciliar Church" which they didn't even know existed, despite each one explicitly referring to the Catholic Church and their authority as its leader.
Oh, the conciliar church certainly does exist, as Fr. Wathen puts it in his book, Who Shall Ascend?:
....The reader is implored to believe that as it is in the spirit of Christian charity that we have been compelled to proclaim the Catholic Church to be the sole and exclusive instrument of salvation for men on earth, it is in the same spirit that we assert the major thesis of this third part, viz., the Conciliar Church is not the Catholic Church, though it is within it, like a fifth column.....It's worthy to note, that Fr. Wathen is actually only saying that which has previously been said by Pope St. Pius X, below in the pope's teaching from Pascendi Dominici Gregis, the only real difference is that today, they are no longer hid, but they are still within:
Gravity of the Situation2. That We make no delay in this matter is rendered necessary especially by the fact that
the partisans of error are to be sought not only among the Church's open enemies;
they lie hid, a thing to be deeply deplored and feared,
in her very bosom and heart, and are the more mischievous, the less conspicuously they appear. We allude, Venerable Brethren, to many who belong to the Catholic laity, nay, and this is far more lamentable, to the ranks of the priesthood itself, who, feigning a love for the Church, lacking the firm protection of philosophy and theology, nay more, thoroughly imbued with the poisonous doctrines taught by the enemies of the Church, and lost to all sense of modesty, vaunt themselves as reformers of the Church; and, forming more boldly into line of attack, assail all that is most sacred in the work of Christ, not sparing even the person of the Divine Redeemer, whom, with sacrilegious daring, they reduce to a simple, mere man.....
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