***From a Catholic POV, Mormons and Jehovah's Witnesses don't believe the same doctrine we do;***
I agree with you on all this. I know that the when a protestant converts to the Catholic faith their baptism in that protestant faith, such as Baptist, or Methodist and Presbyterian is accepted by the Catholic church. Mormon and JW baptism is not.
What I am trying to show is ther are certain church groups that will not accept any protestant or Catholic baptism but you must be re-baptized in their own particular church with the proper mindset, by immersion only after you have run down the proper checklist of things you have to do. The followers of the doctrine of Alexander Campbell come immediatly to mind, although there are some others.
Once again, you are misrepresenting the beliefs of members of churches of Christ. We do not follow Alexander Campbell, we follow Christ. And I know of no member of the church of Christ that claims a church of Christ member has to baptize someone for it to be valid.