I absolutely deny that a person whose public profession of faith is their Hinduism, Pharisaical Judaism, Protestantism, Eastern Schism, etc. can be united to the body of the Church by desire, and in fact united to the soul of the Church.
Such a union would destroy the unity of faith. Many claim that such persons in so-called "good faith" are actually Catholics. You tell me, what are they professing in their day to day lives? What faith are they professing? What places of worship do they visit, what faith do they tell their neighbors they belong to? What faith do they practice? Are you going to tell me with a straight face that such souls are to be counted as Catholic? What of all the quotes above? What of divine light and grace? Will they be enlightened or NOT?