My understanding of the sedes though, is that there is a blanket statement or judgment made across the board that no NO is or could possibly be Catholic. In that case there would be no doubt that their baptism was invalid (beyond whatever year the sedes believe the NO started).
When Christ instituted the sacrament of Baptism, along with the other sacraments. They were instituted by Christ and belong to Christ. But He founded the Catholic Church, and committed His religion to her only. One Lord, One Faith, One Baptism. If the novus ordo person administer Baptism validly, it is because one need not be a priest, therefore if the Baptism was done properly even within the novus ordo, the person is Baptized into the Catholic Church, because they alone own the sacrament, through Christ. The person is not Baptized into novus ordo or Protestant sect but the Catholic church.
Yet, it still must be done properly, which is my point.As Dawn pointed out, there are too many questions these days as to whether it was done properly or not.
Since Baptism could only be administered ONCE, an all out Baptism as you worded it would not be correct, on the chance it was done properly.
CMRI knows the catechism/canon law et al, because they use past encyclicals of past popes, prior to Vatican II for research in all matters of Faith and Morals, as I hope and believe all SV chapels do. Unlike the novus ordo religious, which is why they are not Catholic in the eyes of SV chapels. Many laity there, (novus ordo) I have no doubt know more about Tradition than their so-called Modernist "priest". They, the Modernist are the movement, moving toward the one world religion to go with the one world government.
I wonder what will happen to all the SSPX laity, if their Bishops really do merge fully with novus ordo. I always believe they would not go along, but seeing so many defend novus ordo here, I now have my doubts.
What about you Wallflower would you just follow along, if that happened?