Where do you get the idea that God wants us all to be the same? He has created such immense diversity and variety throughout the natural world, the animal kingdom and within the human race. Why do you think that stops when it comes to sexuality and gender? Just looking at biology alone shows that we were not designed with some strict binary in mind. The male and female sexual organs are analogous/homologous to each other (penis = clitoris, testicles = ovaries, prostate gland = Skene's gland, both have breasts, etc.). Both sexes start out the same in the womb and we all have both male and female hormones within us. Plus, you have intersex, transsexual and transgender people. Biological sex is a continuum or a spectrum rather than a binary. All of this is just natural variation.
Throughout the world's cultures non-heterosexual and gender variant people were viewed as having their own special spiritual and social gifts to add to the community and enrich it. This is true of the Semitic and Greco-Roman cultures that the Abrahamic faiths were born in. They did not share the same views on sexuality and gender that we do now. They had their social mores in regard to sex, but they were not the same as ours. However, they were certainly not binary in their thought and recognized a diversity of sexual and gender identities, which had their place in the society and were not condemned.
The Bible does mention what we'd call queer people (sexually and gender variant people) and in tones that are not in condemnation - just the opposite as they were even celebrated!:
Jesus spoke of "eunuchs", who were what we'd call effeminate gay men or straight trans women (basically males who take the passive role in male/male sex and had a "third gender" status in society):
http://www.well.com/user/aquarius/thesis.htm
One of the earliest Gentile converts to Christianity was a black African eunuch:
http://www.wouldjesusdiscriminate.org/biblical_evidence/early_church.html
David and Jonathan certainly had an intense homoerotic relationship:
http://www.wouldjesusdiscriminate.org/biblical_evidence/david_jonathan.html
Similarly, Ruth and Naomi had a strong sapphic love for each other:
http://www.wouldjesusdiscriminate.org/biblical_evidence/ruth_naomi.html
Of course, you have God Incarnate - Jesus Christ - being born without any heterosexual sex taking place and most Christians hold to the belief that Mary was ever-virgin (making Mary and Joseph's marriage a celibate one); apparently there is a belief in some traditions where Mary is viewed as basically being a true hermaphrodite or otherwise gender variant, as well. There were also examples of what we'd call gay marriages in Christendom for centuries, including one in Spain in the year 1061.
Plus, those 6 verses (yes, only 6 out of thousands!) that seem to be referring to homosexuality are all easily explained away when you know about the cultural context and the original languages.