(Under Construction. For now this page is no more than an unstructured, expanding listing of possibly related posts)
The short answer is that there is no term which is universally acceptable, clear in meaning, fully inclusive and easy to use. In practice, I attempt to get around this by deliberately using a range of terms, avoiding any attempt at precision in their use. In an ideal world, there would simply be no need for labels of any kind.
But we do not live in an ideal world. Of the poor choices available, my first choice is “queer”, used in a very specific sense – that of self-acknowledgement as being included in one or other sexual or gender minority group. For a fuller exposition, see the post Why “Queer”?
The reflex reaction of many people in the Christian Churches to questions of sexuality is simple: sex is only for the purposes of procreation, as demonstrated by “natural law”. This assumption is deeply flawed, both as theology and as empirical fact.
This page aims to present the evidence, from human history, social anthropology and psychology. (The next page considers the evidence from zoology).
It is often claimed that homosexuality is “unnatural”, and is not found in the animal kingdom. This belief is entirely false. The empirical evidence from the field is that same sex genital activity, and also non-procreative heterosexual activity, is widespread through all branches of the animal kingdom. In some species, and for some individuals in others, same sex mating is even more common than the opposite sex variety. Even joint parenting by same sex couples has been widely reported (especially for birds), and is often more successful than opposite sex parenting.
Some key summaries of these points are Confirmed: God is Slightly Gay, and Furred and Feathered Same Sex Parents.
This page elaborates the evidence, with links to posts on specific animals
Marriage & Same – Sex Unions
Marriage Equality: World Update The progress of gay marriage in Europe, Latin America, Asia.
Parenting, Queer Families
Sexuality in Faith
Other Aspects of Queer