What is the doctrine on homosexuality and the final judgement?
This is a very loaded and topical question. I am going to do my best to answer, knowing that a lot of people are going to respond emotionally and not want to hear what I have to say.
Lets start with this quote from our Church leaders: Church Instructs Leaders on Same-Sex Marriage
Changes in the civil law do not, indeed cannot, change the moral law that God has established. God expects us to uphold and keep His commandments regardless of divergent opinions or trends in society. His law of chastity is clear: sexual relations are proper only between a man and a woman who are legally and lawfully wedded as husband and wife. We urge you to review and teach Church members the doctrine contained in “The Family: A Proclamation to the World.”
Just as those who promote same-sex marriage are entitled to civility, the same is true for those who oppose it. The Church insists on its leaders’ and members’ constitutionally protected right to express and advocate religious convictions on marriage, family, and morality free from retaliation or retribution. The Church is also entitled to maintain its standards of moral conduct and good standing for members.
First we have to recognize the difference between homosexual attraction which is a temptation, and a homosexual action which is to act on the temptation. Such action is a sin.
This whole world is full of temptations, being tempted is a part of this life’s experiences (even if we don’t all experience the same temptation). Christ was tempted, he resisted temptation and focused his efforts on doing the will of the Father. That is our example and is the standard we try to meet.
Now we are not perfect like Christ, we will sin by falling into one(or more) of these temptations that face us. When we do we need to repent and try to do better.
Homosexuality is not exempt from this pattern. Those who suffer from this temptation need to resist, and should they fail to resist the temptations they face, they need to repent of their sins just like everyone else. Members who do not face this temptation need to be just as supportive of those struggling to overcome a same sex attraction, as they would support their brother or sister struggling with any other temptation.
The problem we all face with strong temptation is to try to justify why it is OK to give in. To find reason to call it not a sin, or not that bad. When we do this we stop trying to repent and become an unrepentant sinner. This is why we all need to support each other, not in sin, but in over coming sin.
Let me give an example… Let is say my temptation is pride… pride is a sin, and I know this, but lets say I struggle with it daily anyways. Some days I give in and my pride rules, so I repent and I resume struggling. But it is very hard and I grow tired and weak… And in that moment of weakness I hear things like “God made me this way so how can it be wrong” Or “There are bigger and more more important things then that” or something else that tries to convince me I don’t need to follow God or that following God is just too hard. That would be another temptation and it is very attractive.
If I follow it though, I will set something other than Christ as my example. And I will become more and more alienated from God.
Now you have asked about final judgement and that is simple really. All those who have followed Christ, repented of their transgression (which are quite likely to be many) will do well no matter how hard the struggle was to get there. Those who have alienated themselves from God, who have not repented, who took the world as their example, will not do so well.
The details of course belong to God, but the general outline I gave is how it will work for everyone no matter temptation.