And so continues the ongoing disagreement whether entrance into the church comprising the saved is through the door of Christ, or whether entrance into Christ is through the ministrations of a body that on earth features sinners of various degrees. All I can say is that the temptation of a church’s declarations to become self serving is immense.
Off topic, but just to clarify something not reflected in those quotations. The Catholic church doesn’t recognize any distinction between Catholic, Orthodox, or Protestant baptism. As far as the Catholic Church is concerned, if you are baptized, no matter by who, you are by that very act a member of the Catholic Church in substance if not in name. Always keep that in mind when you hear “outside the Church there is no salvation”.