My daughter-in-law became Catholic before she married my son. I helped to find a class for her and I contacted the parish close to her college. I told the priest that she was baptized Presbyterian and he said, "That is pretty close, yes her baptism would be accepted."
My understanding is, with water in the name of the triune God, is sufficent.
We all are much better off by looking at what we share and go from there than to purposely distance ourselves from others.
Those who talk about "thirty thousand denominations" (or whatever the number pulled out of a dark place is this year) seem to be deliberately misunderstanding and misrepresenting protestant ecclesiology. See, for an example, the oft repeated chart Salvation reproduced above.
I, as a Presbyterian, don't think the Lutherans and the Baptists are not Christians and in a false church. The Catholic arguers do seem to think that.
Well, they are just plain wrong.
A number of Protestant churches say the Apostle's Creed and all say the Our Father. Each Protestant denomination holds onto certain aspects that are also shared by Catholics. That is what we should be concentrating on.
We are separated for reasons only God knows.
It will be to His Glory when we all put away our differences.
Jesus would have it no other way.