“The Catholic Church...does not consider it to be a Christian faith and will not accept their baptism.”
Just curious - what other faith group does the Catholic Church accept the baptism from? Quakers, Lutherans, Methodists, etc.? Any of the mainstream groups?
The Catholic, Lutheran, Anglican, Presbyterian and Methodist Churches accept baptism performed by other denominations within this group as valid, subject to certain conditions, including the use of the Trinitarian formula. It is only possible to be baptized once, thus people with valid baptisms from other denominations may not be baptized again upon conversion or transfer. Such people are accepted upon making a profession of faith and, if they have not yet validly received the sacrament of confirmation or chrismation, by being confirmed. In some cases it can be difficult to decide if the original baptism was in fact valid; if there is doubt, conditional baptism is administered, with a formula on the lines of “If you are not yet baptized, I baptize you….”[133]
[133]^ Code of Canon Law, canon 869; cf. New Commentary on the Code of Canon Law By John P. Beal, James A. Coriden, Thomas J., pp. 1057-1059.
To the best of my knowledge, the Catholic Church will recognize the baptisms of other Christian denomination who’s doctrines are generally in line with the fundamentals of overall Christian faith - Trinity, Salvation, etc. and the method of baptism - use of the Trinitarian formula, water, etc. So the acceptance is rather broad. The best official statement is found here
http://www.intratext.com/IXT/ENG0017/_P2W.HTM
which basically says a non-catholic baptism can be accepted unless there is serious reason for doubting the validity of that baptism.
The interesting fact is that the mormon church is the only one that the Catholic Church as specifically singled out by name as having an invalid baptism.