Which commonly bring the accusation that we believe we are "right" while everyone else is "wrong".
Totally untrue.
What we believe is that we are a church (a religion is repository for a theology) that works off of a theology that was restored to the church that teaches things long since lost or forgotten.
People who practice what they believe are doing what they can and the Atonement of the Lord Jesus Christ will allow them (and everyone) the opportunity to enjoy the blessing of the restored gospel. In this life or the next.
We believe that there is much more to our existence than this mortality (this mortality being very important). We existed before we came here and we will continue to exist and grow after this life.
We believe that we are the only church which holds the priesthood of God and are able to bestow those priesthood blessings onto others. We believe that the original Church of Jesus Christ that Jesus established fell into a state of apostasy and needed to be restored. We believe that God restored his church through the prophet Joseph Smith and that God told the prophet Joseph Smith the following:
Joseph Smith History 1: 16-20
16 But, exerting all my powers to call upon God to deliver me out of the power of this enemy which had seized upon me, and at the very moment when I was ready to sink into despair and abandon myself to destruction—not to an imaginary ruin, but to the power of some actual being from the unseen world, who had such marvelous power as I had never before felt in any being—just at this moment of great alarm, I saw a pillar of light exactly over my head, above the brightness of the sun, which descended gradually until it fell upon me.
17 It no sooner appeared than I found myself delivered from the enemy which held me bound. When the light rested upon me I saw two Personages, whose brightness and glory defy all description, standing above me in the air. One of them spake unto me, calling me by name and said, pointing to the other—
This is My Beloved Son. Hear Him!
18 My object in going to inquire of the Lord was to know which of all the sects was right, that I might know which to join. No sooner, therefore, did I get possession of myself, so as to be able to speak, than I asked the Personages who stood above me in the light, which of all the sects was right (for at this time it had never entered into my heart that all were wrong)—and which I should join.
19 I was answered that I must join none of them, for they were all wrong; and the Personage who addressed me said that all their creeds were an abomination in his sight; that those professors were all corrupt; that: “they draw near to me with their lips, but their hearts are far from me, they teach for doctrines the commandments of men, having a form of godliness, but they deny the power thereof.”
20 He again forbade me to join with any of them; and many other things did he say unto me, which I cannot write at this time. When I came to myself again, I found myself lying on my back, looking up into heaven. When the light had departed, I had no strength; but soon recovering in some degree, I went home. And as I leaned up to the fireplace, mother inquired what the matter was. I replied, “Never mind, all is well—I am well enough off.” I then said to my mother, “I have learned for myself that Presbyterianism is not true.” It seems as though the adversary was aware, at a very early period of my life, that I was destined to prove a disturber and an annoyer of his kingdom; else why should the powers of darkness combine against me? Why the opposition and persecution that arose against me, almost in my infancy?
Its not that all other Christian sects do not have any truth but that they do error in many ways in so much that God does not recognize them as His. They draw near him with their lips but their hearts are far from Him. They are apostate and are considered an abomination in His sight. According to the revelation to Joseph Smith, these other Christian denominations were not God's true church. Through the prophet Joseph Smith, God restored his only true church upon the face of the earth.
Not everything other churches say is false. But they are not the path that the Lord would have them follow. Without the true priesthood of God, their baptisms are not valid and other teachings such as faith without works are not correct. However what you say is true that those who never have the opportunity to accept the true gospel in this life may have that opportunity in the next life. We know that Jesus went and preached to the spirits that were dead and set up his gospel in the afterlife. So the opportunity is not subject to this life only. I believe that since it is mentioned in scripture that if we commit certain sins that we will not have forgiveness in this world nor in the world to come, that there is probably a degree of forgiveness to others who do not commit unforgiveable sins in the world to come. God, in scripture, has mentioned that there is eternal punishment but he has also stated the following:
Doctrine and Covenants 19:6-12
6 Nevertheless, it is not written that there shall be no end to this torment, but it is written
endless torment.
7 Again, it is written
eternal damnation; wherefore it is more express than other scriptures, that it might work upon the hearts of the children of men, altogether for my name’s glory.
8 Wherefore, I will explain unto you this mystery, for it is meet unto you to know even as mine apostles.
9 I speak unto you that are chosen in this thing, even as one, that you may enter into my rest.
10 For, behold, the mystery of godliness, how great is it! For, behold, I am endless, and the punishment which is given from my hand is endless punishment, for Endless is my name. Wherefore—
11 Eternal punishment is God’s punishment.
12 Endless punishment is God’s punishment.
From this I believe that for most, there will be forgiveness of sin in the world to come and possibly progression. However, for those who become the sons of Perdition, I don't think that they will receive forgiveness in this world or the world to come.