Can a homosexual enter into the kingdom of heaven?
Because salvation is by faith alone in Christ alone and we are not saved by our works good or bad, yes, a homosexual person can go to heaven. Having said this, however, there is always the question of whether such a person has faced their sin and truly put their trust in Christ. If they have, then to continue with a homosexual lifestyle is living in rebellion and a believer will eventually experience misery and divine discipline.
The Scripture, which is God-breathed and accurate, gives us God’s declaration concerning this issue. It clearly states that it is sinful and contrary to man’s basic nature and the way God created us. Scripture gives us God’s revelation on this, not to keep us from having fun or from enjoying life, but to protect us from ourselves and the depravity to which we can all go when we seek to live our lives apart from a relationship with Him in the light of the Bible as His index and authority for both belief (doctrine) and practice (behavior).
The Scripture also gives us some strong warnings about having sin (any sin) as the practice, characterization, habit of our lives.
John 3:4-9 Everyone who practices sin also practices lawlessness; indeed, sin is lawlessness. And you know that Jesus was revealed to take away sins, and in him there is no sin. Everyone who resides in him does not sin; everyone who sins has neither seen him nor known him. Little children, let no one deceive you: The one who practices righteousness is righteous, just as Jesus is righteous. The one who practices sin is of the devil, because the devil has been sinning from the beginning. For this purpose the Son of God was revealed: to destroy the works of the devil. Everyone who has been fathered by God does not practice sin, because God's seed resides in him, and thus he is not able to sin, because he has been fathered by God.
(We know he is not simply talking about a one time sin, but something that characterizes a life by John's reference to "practice" in the context, the tense of the Greek verb used here, and the previous discussion of sin in relation to the Christian in 1 John 1:9-2:2.)
If that behavior of sin is the pattern of our lives we have no foundational reason to believe we have truly trusted in Jesus for the forgiveness of our sins. In that case the warning of 2 Corinthians 13:5 to test ourselves to see if we are indeed in the faith is especially important to heed.
So while anyone may be saved from their sin (regardless of what sin or to what extent it has been practiced) by faith in Jesus Christ and His work on their behalf in His death, burial, and resurrection, there are indeed warnings in Scripture that those who have truly been saved do not stay the same. God begins changing our lives as we surrender to His lordship and sanctifying work. We are saved as we are, but we do not stay that way. Remember Jesus' words to the woman caught in adultery after He showed her compassion and forgiveness: "Go and sin no more." (John 8:11) How is that possible? In the power of Christ alone through a surrendered life to Him and His work in one's life.
So then, one would no longer be identified by one's previous identity or slavery to any particular past sin—whether as a drunkard, adulterer, homosexual, thief, covetor, idolator, fornicator, extortioner, etc. Instead we would be now identified as the children of God, Christians, disciples of Jesus Christ. As having been freed from sin, we are a new creation in Christ (2 Cor. 5:17), and He will walk with us day by day to transform our lives as we walk in submission to Him.
1 Corinthians 6:9-11 Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived! The sexually immoral, idolaters, adulterers, passive homosexual partners, practicing homosexuals, thieves, the greedy, drunkards, the verbally abusive, and swindlers will not inherit the kingdom of God. Some of you once lived this way. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God.
Thanks be to God for providing a way for rescue from sin and providing for us to be able to walk in newness of life!
John 3:16-18 For this is the way God loved the world: He gave his one and only Son, so that everyone who believes in him will not perish but have eternal life. For God did not send his Son into the world to condemn the world, but that the world should be saved through him. The one who believes in him is not condemned. The one who does not believe has been condemned already, because he has not believed in the name of the one and only Son of God.
Sam Storms has also done a very good job over here (http://www.samstorms.com/enjoying-god-blog/post/the-unrighteous-will-not-inherit-the-kingdom-of-god) pointing out how these same truths equally apply to adultery, and heterosexual sin. He also helpfully clarifies that having ever committed a homosexual act or a heterosexual sin does not forever exclude one from the kingdom of God. Rather it is the person who has an unrepentant and relishing mindset on immorality, drunkenness, idolatry, etc. that is in view. This passage likewise is not excluding people from the kingdom of God who struggle with these sins. Attraction to sin and action upon it are different matters-- as are reveling in something versus stumbling back into something. May we all depend on God's grace daily so that we gain victory over our temptations. We would recommend you see his article for further thoughtful consideration of these topics and this Scripture.