Anti-Mormon writers use a theory called the Adam-God Theory, with which they make the claim that Mormons believe Adam is God the Father; and also, that within the Mormon faith, this is (or was) a deeply held and secret belief.
The theory stems from a sermon delivered by Brigham Young on April 9, 1852. Here is the passage in question.
Now hear it, O inhabitants of the earth, Jew and Gentile, Saint and sinner! When our father Adam came into the garden of Eden, he came into it with a celestial body, and brought Eve, one of his wives, with him. He helped to make and organize this world. He is Michael, the Archangel, the Ancient of Days! about whom holy men have written and spoken--He is our Father and our God, and the only God with whom we have to do. Every man upon the earth, professing Christians or non-professing, must hear it, and will know it sooner or later.
…Jesus, our elder brother, was begotten in the flesh by the same character that was in the garden of Eden, and who is our Father in Heaven. (JD 1:50-51)
This is a very straightforward statement and, as far as I know, the only one of its kind. There is no easy way of getting around what it says. Though it is possible to put this statement in a context consistent with Mormons beliefs, it would require a degree of verbal and theological gymnastics to do so. But only Mormons would be interested in that, so I won’t bother.
So how can Mormons ignore the statement “[Adam is] our Father and our God, and the only God with whom we have to do,” as well as “Jesus, our elder brother, was begotten in the flesh by the same character that was in the garden of Eden”?--After all, we do not believe that Adam is God the Father or that Adam conceived Jesus. This brings up a more important, and more interesting, aspect of Mormon theology: degrees of doctrinal confidence. What follows is a somewhat loose explanation of this concept.
In Mormon theology there are core beliefs that are well defined and regarded as sacrosanct. There also exist beliefs that, though common among Mormons, are based upon tradition--what could be called popular Mormonism. At the center of doctrinal certainty is the cannon of scripture, the accepted revelations of the prophets. As far as other beliefs are concerned, repeatability and context should be considered: If something does not survive the test of time then within common LDS sensibilities there is little feeling of obligation toward it. Context must also be applied. For example, something the president of the church says to a reporter is not necessarily authoritative. These criteria can be applied to the Adam-God teaching. There seems to be only one instance of it (at least in public) and from other sermons it is clear that Brigham Young correctly understands the relationship between God and Adam: “We believe that he[, God,] made Adam after his own image and likeness” (JD 10, p. 231); and “We are all the children of Adam and Eve, and they and we are the offspring of Him who dwells in the heavens” (JD 13, p. 312). In applying repeatability and the test of time to the Adam-God theory the conclusion is that it can safely be ignored.
At best the Adam-God theory is nothing more than a bizarre thing Brigham Young once said--he said several strange things. At worst it was theory he tried to inject into Mormonism that never caught on. Whichever the case, the Adam-God theory was never part of mainstream LDS beliefs.
There are three possible reasons that non-Mormon Christians take Brigham Young’s statement the way they do. The first is that most anti-Mormon writers have an ax to grind. The second is that Young’s statement is quite plain and very strange. The third is some Christian scholars have equated Michael with Christ  and most consider the Ancient of Days to be God ; but in Mormon beliefs Adam is both the Ancient of Days and Michael the archangel (D&C 27:11).
 “The earlier Protestant scholars usually identified Michael with the preincarnate Christ, finding support for their view, not only in the juxtaposition of the ‘child’ and the archangel in Rev 12, but also in the attributes ascribed to him in Daniel” (“Michael”, International Standard Bible Encyclopedia, 1915)
The Christian writer Albert Barnes wrote, “There have been very various opinions as to who Michael is. Many Protestant interpreters have supposed that Christ is meant.” (Albert Barnes’ Notes on the Bible, commentary on Rev. 12:7).
 About Ancient of Days: “An expression applied to Jehovah three times in the vision of Daniel (Dan. 7:9, Dan. 7:13, Dan. 7:22) in the sense of eternal. In contrast with all earthly kings, his days are past reckoning” (“Ancient of Days”, Easton’s Bible Dictionary).