T.P. the reason Mormonism is not Christian has nothing to do with whether Mormons sing Christmas carols. It has to do with the fact that Christianity is a monotheistic religion and Mormonism teaches that there are many gods. There are many other differences, but the monotheism/polytheism thing is a deal-breaker.
But just because Mormonism is not a Christian religion doesn't mean we can't be friends.
I sang a LOT of carols before I was a Christian!
I understand that orthodox Christianity does not accept Mormonism as Christian. And I understand that our teaching of the nature of God and our relationship to him is the key reason for this.
But you would be amazed at the examples provided on this forum as to why we are not Christian, including the aforementioned "not singing Christmas carols" along with "not attending church on Christmas day" and "not having an Easter Sunrise service" and "using water in the sacrament [of the Lord's Supper]."
Those arguments are so absurd that I usually cannot let them stand unchallenged. It also makes me wonder about the motives of those making the claims. Hence my "lies for Jesus" statement.
As for the theological differences, for the most part we have to acknowledge that they exist and attempt to correct the worst misstatements. But in the end, it boils down to who we say God is, and who (the collective) you say God is. We probably have to agree to disagree.
Having said that, I also understand the intentions of those who feel that they need to protect others from falling into the "trap of Mormonism." I just wish it could be done in a more civil, mature (and indeed, friendly) manner.