When reading this question, and the answers that follow, several scriptures came to mind regarding God's feelings. I will list those first.
The last scripture in my answer, I believe may actually answer the question rather directly.
The first was Romans 12:1-2
I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service. And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God.
This scripture clearly asks us, beseeches us actually, to strive to be that which is other than simply acceptable in our culture, but to be holy and acceptable to God.
God makes His views clear for us in 1 Corinthians 6:9-10
Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, not adulterers, nor homosexuals, nor sodomites, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God.
This scripture is also clear regarding God's feelings toward homosexuality. The following verse,
1 Corinthians 6:11
And such were some of you. But you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus and by the Spirit of our God.
This gives us all hope. We are all sinners.
To answer the question, "Why do some Christians believe it is moral to be homosexual?"
We have been warned about the Deceptions of False Teachers in;
2 Peter 2:18-19
For when they speak great swelling words of emptiness, they allure through the lusts of the flesh, through lewdness, the ones who have actually escaped from those who live in error. While they promise them liberty, they themselves are slaves of corruption; for by whom a person is overcome, by him also he is brought into bondage.
There is, unfortunately, a tendency to turn from "unpopular" scripture to attract greater numbers into congregations. There has also been serious discussion of removing the word "virgin" from scripture in regard to Christ's birth for the purpose of attracting more church members.
It seems apparent that some Christians believe homosexuality is moral because they are being fed by false teachers. Scripture is clear.