It's somewhat of a semantic argument in how you define "Christian" but what it boils down to is that most Christian groups accept the baptism of other Christian groups and do not re-baptize upon conversion (for example if I were Methodist and wanted to become Catholic, i would not be re-baptized) but this is not the case for a couple of groups, including Mormons. Most other Christian churches do not accept Mormon baptisms as valid because of specific belief differences regarding the nature of Christ and the Trinity (among other things). I believe that Mormons also do not accept the baptism of other Christian churches though I am not sure specifically why or if there are exceptions.
If I said I believed the teachings of Christ but interpreted those teaching to be the opposite of what all other Christians do would I still be a Christian? I'm not accusing Mormon's of this but just giving an example. I think most Christian groups don't consider Mormons to be Christian (or at least don't accept their baptisms) because interpretation of key scripture and what you are promising to believe and uphold is sufficiently different as to make the baptism mean something different whereas this is not the case if you are going between most of the various Catholic, Orthodox and Protestant groups.
Another example. Muslims believe in Jesus and that he was a prophet and therefore presumably accept his teachings but they don't recognize his divinity. Much like Mormonism, it recognizes the teachings of different prophets (particularly Mohammad in the case of Islam). Islam is a distinct religion from Christianity. Mormons recognize the divinity of Jesus but in a different way than most other Christian groups (this goes back to the Trinity again). Is this difference big enough for Mormonism to be considered a different religion like Judaism or Islam? Why wouldn't Muslims be considered Christians if they believe in Jesus and follow what they believe are his teachings in addition to those of Mohammad? Is simply choosing to call yourself Christian sufficient to make you one? While the specific issues involved may seem esoteric to non-Christians or at least to non-religious people, they are quite important to many Christians, including Mormons.
I think the takeaway here is that whether or not you call Mormons Christians, their beliefs are more significantly different from other Christian denominations than other Christian denominations generally are, not just in what it adds via its own prophets but in how it interprets parts of the Bible that is shared between them.
Well put. It gives some good food for thought.
FYI, you're right. We don't accept other's baptisms, and they don't (as far as I know) accept ours. Mostly coming down to differences in belief for how it's performed and by whom.
How and who might have something to do with it but the more important reason is the rejection of parts of the Nicene Creed by Mormons. This is the key baptismal creed for most other Christians.
From https://en.wikipedia.org/wiki/Nicene_Creed
"Some sects, such as the Church of the New Jerusalem, The Church of Jesus Christ of Latter-day Saints, and the Jehovah's Witnesses explicitly reject some of the statements in the Creed, either because of a non-Trinitarian theology and/or a rejection of historically orthodox Christology."
Yup.
Most Christian churches believe that the Father, Son, and Holy Ghost are one in every way. We believe they are separate physically and have different roles, but are perfectly unified in all they do.
I think that the differences in how and who are probably closer to our reasoning behind why we don't accept other's baptisms, but I could totally understand this being why others don't accept ours.