I wasn't quite sure I understood their points correctly, so I went and looked up the thread you're talking about. Yikes, a thread that's almost 600 posts long, all debating our theology? I wouldn't have the patience for that, frankly. Arguing with people gets rather old after a while. However, answering a few objections isn't too bad.
I'll address your second question first, since it has the shortest answer. They're basically saying that since the "evildoers" in Jeremiah's time were destroying records of his teachings, it makes no sense for Laban to have records that include his teachings. That's not much of an argument, though. There are plenty of arguments against such a position: he wanted to appear
pious; he was simply ignoring Jeremiah; he was unaware that these particular records had some of Jeremiah's teachings; or any number of other plausible motivations. Although many people were persecuting the prophets and destroying their words, you can't draw the conclusion that everyone
who was wicked was acting in exactly the same way, nor that all
copies of prophetic words in their possession would have been destroyed. There's simply not enough evidence to support such a conclusion.
Now, to their other point. It basically boils down to our conception of the Godhead: we believe in three separate personages who are nonetheless united in purpose, while they believe in one Trinity, which is only one being yet three. (I almost got sidetracked on the definition of worshiping an idol, which is not
just "worshiping something that is created," but that's not the main point here.) Because we believe in three distinct personages who are members of the Godhead, some people claim that we are therefore polytheistic, or breaking the commandment "Thou shalt have no other gods before me" (Exodus 20:3
Here are what a few general authorities have to say about the charge of polytheism; I urge you to go read the entire articles I'm linking to, since they go much more in depth on the matter than I can quote here. I'll warn you that this is going to get a bit long, though I've tried to be as brief as possible while still maintaining enough context.
To acknowledge the scriptural evidence that otherwise perfectly united members of the Godhead are nevertheless separate and distinct beings is not to be guilty of polytheism; it is, rather, part of the great revelation Jesus came to deliver concerning the nature of divine beings. Perhaps the Apostle Paul said it best: "Christ Jesus...being in the form of God, thought it not robbery to be equal with God" (Philippians 2:5–6)
- Elder Jeffrey R. Holland, "The Only True God and Jesus Christ Whom He Hath Sent," Nov. 2007 Ensign, pp. 40–42.
A fourth area of misunderstanding among some of our friends in Christianity is that they refer to us as "polytheists," meaning that we believe in a plurality of Gods. Much misunderstanding would be avoided if they understood that we worship only one Godhead, consisting of God the Father, God the Son, and God the Holy Ghost. We believe that the biblical record teaches that God the Father, Jesus Christ, and the Holy Ghost are separate persons. When the Savior was baptized, the Father spoke His approval from heaven, and the Holy Ghost was witnessed to be present by the sign of a dove (see Matt. 3:16â€“17). Likewise the Bible records the prayers of Jesus Christ to our Father in Heaven, a separate being (see John 17:3). We believe this doctrine is taught in the Bible despite what the creeds of other Christian denominations may teach.
- Elder M. Russell Ballard, "Building Bridges of Understanding," Jun. 1998 Ensign, p. 62.
We are Christians because we worship the Christian Godhead, the Christian Trinity. "We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost." (A of F 1:1.) We have no other gods before us. (See Ex. 20:3.) We do not worship prophets or saints, neither of modern nor of ancient times. We pray only to the Father, as the Savior taught during his earthly ministry (see Matt. 6:9â€“13); and this we do only in the name of the Savior. We teach, as the scriptures do, that there is no intermediary between God and man save Jesus Christ, and "none other name given under heaven save it be this Jesus Christ...whereby man can be saved." (2 Ne. 25:20.)
- Elder Robert E. Wells, "We Are Christians Because...," Sep. 1984 Tambuli, p. 7.
A few who aren't general authorities have also done a good job of explaining and defending our doctrine:
The Latter-day Saints are accused of worshiping a "different god" because we do not believe in the traditional Trinity. "We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost" (A of F 1:1) as taught in the New Testament. What Latter-day Saints do not believe is the non-Biblical doctrine formulated by the councils of Nicaea (A.D. 325) and Chalcedon (A.D. 451) centuries after the time of Jesus—the doctrine that God is three coequal persons in one substance or essence. We do not believe it because it is not scriptural. As Harpeŕ’s Bible Dictionary states: "The formal doctrine of the Trinity as it was defined by the great church councils of the fourth and fifth centuries is not to be found in the New Testament."
Jesus didń’t teach the Nicene doctrine of the Trinity. The New Testament writers didń’t have any idea of it. The doctrine itself wasń’t invented until centuries later. So one cań’t say the Latter-day Saints are not true Christians for not accepting it, unless one also excludes Jesus, his disciples, and the New Testament Church, who similarly did not know or teach it.
- Stephen E. Robinson, "Are Mormons Christians?", May 1998 New Era, p. 41.
As the church entered the third century, many ridiculed Christianity because they regarded it as polytheistic—that is, it had a theology of three Gods: the Father, Son, and Holy Ghost. By this time the more sophisticated had rejected polytheistic pagan deities and had become monotheistic, accepting but one God. So the issue for the church was how to make Christian theology accord with respectable opinion.
Tertullian, a lawyer, offered this solution: The true God was composed of immaterial spiritual substance, and though the three personages that comprised the Godhead were distinct, this was only a material manifestation of an invisible God. As for how three persons could be one, it was explained that the persons were legally conceived entities, "just as a corporation is composed of various people though it is not the people." (T. Edgar Lyon, Apostasy to Restoration, Salt Lake City: The Church of Jesus Christ of Latter-day Saints, 1960, p. 113.)
Fusing the ideas of church theologians, such as Irenaeus, Origeu, Tertullian, and Athanasius, the Trinitarian formula of three spirits in one was finally accepted as official doctrine by the council of Nicea in a.d. 325. (Lyon, pp. 144–53; Barker, pp. 249–71.)
- William O. Nelson, "Is the LDS View of God Consistent with the Bible?", Jul. 1987 Ensign, p. 56.
In an effort to satisfy the accusations of Jews who denounced the notion of three Gods (Father, Son and Holy Ghost) as polytheistic, and at the same time incorporate ancient but appealing Greek philosophical concepts of an all-powerful moving force in the universe, the Christian church began to redefine the Father, Son and Holy Spirit. One classic work describes the intersection of Christian theology and Greek philosophy: "It is impossible for any one, whether he be a student of history or no, to fail to notice a difference of both form and content between the sermons on the Mount and the Nicene Creed. ... The one belongs to a world of Syrian peasants, the other to a world of Greek philosophers. ... The religion which our Lord preached ... took the Jewish conception of a Father in heaven, and gave it a new meaning." In short, "Greek Christianity of the fourth century was rooted in Hellenism. The Greek minds which had been ripening for Christianity had absorbed new ideas and new motives" (Edwin Hatch, The Influence of Greek Ideas on Christianity (Gloucester, Massachusetts: Peter Smith Publishers, 1970), 1, 4â€“5.)
- Robert L. Millet, "What Mormons Believe About Jesus Christ," from the newsroom of lds.org.
Allow me to unequivocally state in the clearest terms I know of: The Church of Jesus Christ of Latter-day Saints does not believe or teach that Jesus is "just one" of countless other gods. This has never been taught or believed, nor is it today. ... The Old Testament and the New Testament are consistent in proclaiming the existence of multiple "gods." However, Latter-day Saints do not recognize any other god as "our God." "To us, there is but one God, the Father," and "one Lord, Jesus Christ." ... And does this make Mormons polytheistic? Not unless they started worshiping other Gods, which is not the case. We place no other god before God, as commanded in Exodus 20:3.
- Cooper Johnson, "Mormons--Can They Be Considered Christians?", The Foundation for Apologetic Information and Research. (This article is particularly focused on logical arguments and scriptural examples.)
I think you probably get the point. And as I mentioned before, there's a lot more if you follow up and read each of these articles. I simply couldn't quote everything I wanted to.
Hopefully this is enough to help you figure it out yourself, and explain our beliefs to anyone who is actually trying to understand them. That's the key difference between argument or debate and meaningful dialog: if the parties involved are willing to carefully listen and try to understand each other, whether or not they agree in the end. Good luck!