I'm a "Feeneyite". In a nutshell, here's what we believe (but, of course, I am only speaking for myself here):
1) Sacramental Baptism confers grace. So does "Baptism of Desire" or "desire for Baptism," if you wish. Saint Thomas taught this explicitly; in fact, the Angelic Doctor taught that a catechumen who desired sacramental Baptism but who died without it would have to suffer the temporal consequences of his/her sins in Purgatory, which would have been cleansed if that individual had lived to receive sacramental Baptism.
2) The One and Triune God can being sacramental Baptism to whomever He wills. God is omnipotent, so He can bring sacramental Baptism to anyone who truly desires such and/or is worthy of it. Doing so would in no way be contrary to His Perfect nature.
3) Given God's omnipotence, to say that someone, anyone, was never sacramentally Baptized is to "prove a negative," a "cosmic" one, in fact. Try to prove that someone like Osama bin Laden was never sacramentally baptized in his infancy, as "anyone whatsoever" can baptize. Since, for an infant, a valid baptism is always a fruitful one, bin Landen would have been a Christian for at least some portion of his life. Saint Thomas extended to angels the capacity to administer the Sacraments, which occurred at Fatima.
4) Sacramental Baptism places an indelible mark on a person's soul. No one disputes this. For someone like bin Landen, if he was baptized in his infancy, he died with the character of Baptism on his soul.
5) Salutary repentance is always a possibility. Just as God can raised people from the dead, so, too, He can grant them a final opportunity at "death's door" to embrace the One True Faith.
6) Submission to the Roman Pontiff is necessary for salvation. Such was explicitly stated at the Fifth Lateran Council, "since subjection to the Roman pontiff is necessary for salvation for all Christ's faithful, as we are taught by the testimony of both sacred scripture and the holy fathers, and as is declared by the constitution of pope Boniface VIII of happy memory, also our predecessor, which begins Unam sanctam..." No 'wiggle room' on this one; this is a historical fact as much as a dogmatic one.