This is usually seen as the number one reason for excluding "Mormons" from the lexicon. The problem is twofold. First, the Trinitarian concept was a rather late theological concept. Before, that were any number of non-Trinitarian concepts of Jesus and his relationship to God. Admittedly, the most talked about are the ones that rejected Jesus' divinity. That is something that even Mormons would consider false and suspect for inclusion in the Christian demographic. But, there were still others that believed in divine subordination of Jesus to God rather than fusing them together. The only reason for the exclusion today is because of tradition built from an iron fisted council in the Third Century after Jesus and his Apostles were long dead. As the book Lost Christianities by Bart D. Ehrman suggests, there were many Christian viewpoints of considerable scope and variety. Any number of them could have defined what we now know as Christianity. It is only through a quirk of history, theological wars, and suppression has a seemingly unified Christianity developed.
The second problem is that the Trinity is not particularly Biblical, no matter how much some have continued to argue otherwise. This is not to say there are not Scriptures that bolster the general idea. However, there are plenty of equally commanding Scriptures that can show another possible belief about Jesus' relationship to God. It is beyond the scope of this article to get into that. Plenty of other people, Mormon and non-Mormon (such as Nicene Creed and Truth about the Trinity. ), have discussed the topic. The point is that the Bible doesn't exactly show who is or isn't a Christian beyond the broadest of meanings.
The Book of Mormon and other Scriptures
The idea that a belief in other Scriptures is a prelude to non-Christian identity is problematic in the same way as Trinitary beliefs. Before the Constantine takeover, there were many Christians with many different Scriptures. Once again, "Lost Christianities" shows how delicate a balance the Bible in its present form is to what might have been. Even today there are still argumens over what books should or shouldn't be in the Bible by Orthodox Christians. This is especially the case if considering Catholics vs. Protestants with the so-called apocrypha.
Besides, the Book of Mormon has even been characterized as uber-Christian by the very critics who argue against the Christian self-identification. I will not go so far as to say the recent label of "Another Testament of Jesus Christ" says anything for its Christianity. However, its original introduction still contains the phrase "to the convincing of the Jew and the Gentile that Jesus is the Christ, the Eternal God, manefesting Himself to all nations." The Doctrine and Covenants is no less devoid of Christian statements such as from section 20:
21 Wherefore, the Almighty God gave his Only Begotten Son, as it is written in those scriptures which have been given of him.
22 He suffered temptations but gave no heed unto them.
23 He was crucified, died, and rose again the third day;
24 And aascended into heaven, to sit down on the right hand of the Father, to reign with almighty power according to the will of the Father;
25 That as many as would believe and be baptized in his holy name, and endure in faith to the end, should be saved—
26 Not only those who believed after he came in the meridian of time, in the flesh, but all those from the beginning, even as many as were before he came, who believed in the words of the holy prophets, who spake as they were inspired by the gift of the Holy Ghost, who truly testified of him in all things, should have eternal life,
27 As well as those who should come after, who should believe in the gifts and callings of God by the Holy Ghost, which beareth record of the Father and of the Son;
28 Which Father, Son, and Holy Ghost are one God, infinite and eternal, without end. Amen.
29 And we know that all men must repent and believe on the name of Jesus Christ, and worship the Father in his name, and endure in faith on his name to the end, or they cannot be saved in the kingdom of God.
30 And we know that justification through the grace of our Lord and Savior Jesus Christ is just and true;
31 And we know also, that sanctification through the grace of our Lord and Savior Jesus Christ is just and true, to all those who love and serve God with all their mights, minds, and strength.
32 But there is a possibility that man may fall from grace and depart from the living God;
33 Therefore let the church take heed and pray always, lest they fall into temptation;
34 Yea, and even let those who are sanctified take heed also.
35 And we know that these things are true and according to the revelations of John, neither adding to, nor diminishing from the prophecy of his book, the holy scriptures, or the revelations of God which shall come hereafter by the gift and power of the Holy Ghost, the voice of God, or the ministering of angels.
36 And the Lord God has spoken it; and honor, power and glory be rendered to his holy name, both now and ever. Amen.
It is true that Mormons reject other Christian's baptism. That they would decide to reject Mormon baptisms as legit shouldn't be bothersome. However, this is understandable only if one is arguing from an authoritative, rather than theological, standpoint. The idea of not accepting other baptisms isn't because of what one believes, but by what authority one holds. Mormons simply believe they have been given the authority to act in the name of God and that other Christian denominations do not.
It is not much different than what most Protestants think of Catholics. Then again, there are many Protestants who don't think Catholics are Christians; an even more dubious exclusion. Interesting enough, there are some Christians who don't believe in baptisms at all, even if they accept the idea of such a practice. Never in 1000 years would Mormons not consider others as Christians simply because of a matters of authority. After all, the Christian religion is still splintered over that very topic or there wouldn't be so many different denominations (that isn't the only reason, but it basically boils down to who has the authority to interpret doctrine and practice).
There is much more that could be said on the subject. The book Are Mormons Christians by Stephen E. Robinson is more detailed and focused on the issue. To refuse the title "Christian" to Mormons, or think it a recent ruse, is to be either ignorant of what Mormons believe or extremist sectarian. It is true that we have different ideas about Jesus Christ than most mainstreamers officially accept, but ther are plenty of Christians ( Marcus Borg comes to mind) who could be defined as less Christian than Mormons are, yet still undisputedly hold that title. A belief in a divine Jesus Christ is more than just theology for Mormons. He defines our very lives as much as any mainline Christian. To deny that Mormons are Chrisitans is to do more than argue theology. It is an insult, and those who refuse to acknowedge the Mormon self-identification know it!
Note: see Understanding the Godhead for a discussion of what Mormons believe about the relationship of Father, Son, and Holy Ghost.