Very good points being made here. I'll add a couple from my perspective (and I am a Christian).
It's Easy for You to Judge..
It is very easy for straights to rant on about how homosex is vile and the gays all have to repent or go to hell. Easy because they know that they will never face that particular temptation, so it costs them nothing to be as harsh as possible. It reminds me of how Jesus condemned the church elites of his day for forcing the people to follow religious rules that they themselves would never be able to keep. ("Like tying a millstone around their necks" was the way he put it.)
However, if you bring up something that Jesus says very plainly, like for example "It is easier for a camel to go through the eye of a needle than for a rich man to get into heaven", then these same people suddenly become very quiet. A literal interpretation of the Bible no longer seems like such a good idea because we are now talking about something that actually might apply to them.
Homosexuals: "Perverts" or "Inverts"?
Next, put the writing of the Bible in this context: Until around 1860, everyone assumed that every person was heterosexual - but some "deviants" insisted on having sex with persons of their own gender. They figured that sometimes these "perverts" became so twisted up inside that they actually preferred same-sex to opposite-sex activity.
It wasn't until the middle of the 19th Century that a scientist saw a pattern in the men in her case studies, and suggested that maybe these people weren't naturally opposite-sex oriented at all, but instead experienced an "inverted" sexuality. They were normal in all aspects, except they were attracted to and formed relationships with men and never women.
And then it wasn't until the 1960's that this concept of differing sexual orientations started moving into popular culture and thought. Today, most people take for granted this idea that many people are straight, but that some people are gay.
Mind the Gap
My point here is that there is a cultural gap between today's Bible readers, and the authors of the ancient texts. When the Bible writers discuss "homosexuals", they are talking about straight people (because they assumed that everyone was straight), having gay sex with each other in various specific instances that they found in their culture. Some examples from biblical times are male prostitutes, pagan worship ceremonies, and the Greek man-boy "apprentice with benefits" relationships. It would never have entered their minds that there were people for whom falling in love with someone of the same sex was as natural as heterosexual love. (They also didn't know that the world is round and that the earth spins around the sun, not the other way around. So, there's a long list of things they didn't know about and couldn't be expected to comment on.)
However when we modern readers see the word "homosexuals" in the Bible, we think of our current understanding of gay people: men who are attracted to and fall in love with men, and women with women. And so we easily misinterpret the passages because the writer was addressing one situation, (temple prostitutes, for example), but we are thinking that they are talking about something else entirely (all gay people).
Easy Answers = Wrong Answers
If we allow the ancient writers to be bind to the actual workings of the solar system, we also have to allow that they were blind on the concept of sexual orientation. Contemporary people are not reading the Bible for guidance on how to deal with temple prostitues or boy apprentices. They are looking for answers on what to do about gay people who will never be attracted to the opposite sex, and just want a home and a life with someone they can love.
That issue is not addressed anywhere directly in the Bible. Christians who want guidance on that topic will have to gather together what the Bible teaches about God's love, grace, and justice and figure things out for themselves.