Let me take a stab at addressing your questions…
Yes and No. The LDS form of *baptism * is not recognized as a valid form of baptism in the Catholic Church because the LDS doctrinal understanding of the triune nature of God is not in accordance with the nearly universal christian understanding of the Trinity accepted by the Catholic Church. Because the LDS doctrine is so unique in its teaching on the trinity, the baptism performed by the LDS church is not recognized as a valid form of baptism. Thus, LDS members who have only been baptised in the LDS church must - in addition to receiving the other sacraments of initiation, also receive a validly recognized baptism.
Your question assumes that to be a “christian” one must have received a valid baptism. To some extent that is technically correct. However, there are different forms of baptism in addition to the normal water baptism. There is baptism of desire and baptism of blood. However, if a “christian” is defined as simply a follower of Christ, then to the extent a member of the LDS church can call himself a follower of Christ, they are christian.
Here’s a link to Baptism in the CCC: Catechism of the Catholic Church
[quote=Studens]If it is true, why is it so? (It seems to me the average Latter-day Saint would not need the same kind of instruction as your average Southeast Asian or Amazonian native.)
Instruction is not the issue. The issue is one of valid reception of the sacraments of initiation into the Church. Most non-catholic christian denominations have an understanding of the trinity that is in line with the Catholic understanding and, therefore, the baptism they received in their denomination is accepted and recognized by the Catholic Church. On the other hand, LDS members have not received a valid baptism, even if their time spent studying the scriptures might be greater than, say, a Lutheran convert to Catholicism. The amount of instruction is not the problem. The problem comes from the doctrinal differences between the LDS and Catholic Church.
[quote=Studens]Furthermore, if it is true, what other groups (if any) that identify themselves as Christian are not considered Christian by the Catholic Church for purposes of conversion?
Again, I think there needs to be a distinction drawn between whether or not one is considered a “christian” and whether or not one has received a valid baptism. If a “christian” is simply a follower of Christ, then LDS members are “christians.” But if by using the term you mean that a person has received a valid baptism, then the Catholic Church does not recognize any baptism that is not trinitarian. Thus, e.g. JW baptisms are also not valid because they also do not accept the Trinitiarian nature of God. Also not accepted are baptisms performed solely “in the name of Jesus Christ” as opposed to in the name of the Father, Son, and Holy Spirit.
[quote=Studens]If Latter-day Saints are not considered Christians for conversion purposes, does that mean that there is no difference whatsoever between the conversion process prescribed for Latter-day Saints and that prescribed for, say, the aforementioned Amazonian native?
No. The two persons’ conversion experiences would - I imagine - be quite different on a personal level. However, it is true that both the LDS member and the Amazonian native would have to receive baptism in addition to the other sacraments of initiation, whereas, a convert who was baptised in the Lutheran Church, for example, would not have to receive baptism because the baptism received in the Lutheran Church would be recognized as valid.
[quote=Studens]And finally, what about Catholics who become Latter-day Saints and then later decide they want to return to the Catholic Church?
They are already baptised, and would not have to be re-baptised. Catholics believe in one baptism for the forgiveness of sins. There is nothing a person could do to lose the grace of baptism. (See the link posted above)
I hope this helps.