The OP quotes Bishop Barron as stating, “Vatican II clearly teaches that someone outside the Christian Faith can be saved.” So, your claim that “Again, faith in Christ before judgment is necessary for salvation” is seemingly at odds with the Bishop’s statement, unless (again) you simply mean in an ultimate sense all faith given to any and all people, irrespective of their religion, has God’s grace as the source and cause of the faith. Which, as I said, is true enough. Nevertheless, from the Muslim’s perspective, the proximate cause of his salvation is his Muslim faith, even though in an ultimate sense, God’s grace is extended to the Muslim, which is the primary cause of his salvation, as “God desires that all men be saved and come to a knowledge of the truth” (not just the men who have access to the privileged route of Christianity).
This is not relativism, which would preclude any faith being “privileged,” and would entail that they are all on a par with each other…