Thank you for your extensive and well thought out reply.
The bottom line is, then, permit me to paraphrase, that the Catholic Church teaches baptismal regeneration, and the Catholic Church is the entity which administers baptism.
Therefore, there is no regeneration without the Church, and no salvation is possible outside of the Church, correct?
I am actually discussing this very topic with Catholic relatives who say that I am incorrect.
This part of the discussion is beyond my pay scale, but if it helps any, the (old-school, not silly liberal) priests who baptized my daughters and oversaw our pre-baptism classes made it very clear that any and all Christian baptisms were equal - no need for Catholic-brand holy water or anything like that.
In the eyes of the Catholic Church, any baptism in the Trinitary form of Matthew 28:19 is sufficient.
The bottom line is, then, permit me to paraphrase, that The Church teaches baptismal regeneration, and The Church is the entity which administers baptism - that is The Apostolic Church (Orthodox, Orientals, etc.) and Church doctrines have pointed out the validity of certain groups among what we call “Protestants” — it’s so difficult to say who is or isn’t, so we do not label all “Protestants” the same and we don’t make it our business to say “you’re in and you’re out”