How are people caught up in cults not saved? For example, do you think Roman Catholics are not saved, or Seventh Day Adventists, etc. - how? (I don't think they are, but am unable to explain why. Can you help me give an explanation to them/others?)

Salvation is simply realizing that there is a living God, that we do by nature things that are contrary to His will, and that we must turn from ourselves and trust in Him (Jesus-God incarnate) and Him alone for our eternal salvation. A cult, defined simply in terms of practical usage for these purposes, is a group of people who do not believe this, or believe it in a modified way that renders it of none or lessened effect. I am restricting this definition to those possessing at least some affinity for Christ, so Muslims, Hindus and other world religions will not be discussed. But among this high level classification there are major differences.

The worst cults in my view are Mormons and Jehovah's Witnesses. These two groups deny that Jesus was the living God incarnate, but rather teach that He was a lesser created god. Belief that Jesus is God in the personage of the Son, and is coeternal with the father (John 1:1-18 [1] In the beginning was the Word, and the Word was with God, and the Word was God. [2] The same was in the beginning with God. [3] All things were made by him; and without him was not any thing made that was made. [4] In him was life; and the life was the light of men. [5] And the light shineth in darkness; and the darkness comprehended it not. [6] There was a man sent from God, whose name was John. [7] The same came for a witness, to bear witness of the Light, that all men through him might believe. [8] He was not that Light, but was sent to bear witness of that Light. [9] That was the true Light, which lighteth every man that cometh into the world. [10] He was in the world, and the world was made by him, and the world knew him not. [11] He came unto his own, and his own received him not. [12] But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: [13] Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. [14] And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth. [15] John bare witness of him, and cried, saying, This was he of whom I spake, He that cometh after me is preferred before me: for he was before me. [16] And of his fulness have all we received, and grace for grace. [17] For the law was given by Moses, but grace and truth came by Jesus Christ. [18] No man hath seen God at any time, the only begotten Son, which is in the bosom of the Father, he hath declared him.
See All...) is central to the issue. This belief knocks out every other religion on the planet. God gave us this distinction so that we may clearly discern from the counterfeits. This is elemental and fundamental to salvation. Mormons and Jehovah's Witnesses believe Jesus was "a" [g]od, not "the" [G]od. Seventh Day Adventists and Roman Catholics are of a different vein. They add law keeping and works (or stated another way, the righteousness of man) to salvation. I would also include the Church of Christ in the list because they add the work of baptism to salvation (Adventists add Sabbath keeping, and Catholics too many to list). Nothing is more clearly refuted in scripture than this. The whole book of Galatians is completely dedicated to this topic, as are major portions of many other books of the New Testament.

Along the lines of works based salvation, a few denominations are worthy of an [dis]honorable mention. Groups like the Church of God (Pentecostal, Apostolic, etc.), including "Free Will" Baptists, teach a form of implicit works based salvation, although I have found that many in these denominations do not believe this. While these groups do not specify which laws and works are necessary, they imply they are because they indicate that your actions can cause you to lose your salvation. The implication is that you can earn your way out of it, so to speak. But most of these groups are more often characterized as being "cultic" based on their teaching that apostolic gifts are still active in the church today. Technically, they are at fault for placing too much emphasis on works, and too little on the sufficiency of Christ. However, I do not consider their error as egregious as the aforementioned groups.

With that said, I do believe there are some people who come to a saving knowledge of Christ in the denominations that add works. But this is in spite of their teachings, and not necessarily a direct result of them. All we must do to be saved is trust in Jesus as our personal savior. Of course I say this in the sense that Jesus is God. If you have done that, you are saved. He has given His word. But groups that deny the deity of Christ are leading lost souls to eternal damnation. Also, denominations that add works to the gospel of Christ are preaching a gospel that is accursed of God (Galatians 1:8But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed.
See All...). So, by definition, these groups must be leading some if not many astray.

Hopefully this was not too complex or long to be helpful. In the final analysis, any group that affiliates itself with Christ but doesn't profess Jesus as God and teach His sufficiency alone for salvation is a cult in my mind.