The conservatives have a rigidly deterministic view of biology. Sex seems pretty simple. Men are XY, women are XX. You get a Y chromosome from Dad, you're a boy. You get an X chromosome, you're a girl.
Mostly, but not always.
Due to defects in chromosome segregation, it's possible to be XYY. These individuals are male (and pretty indistinguishable from "normal" males; attempts to correlate extra Y chromosomes with violent behavior were discredited years ago).
XXY chromosomes give rise to Klinefelter's Syndrome. These patients are male, but generally have reduced testicular function and increased levels of female sex hormones. They are generally infertile.
By contrast, XXX females have relatively few symptoms and may not even be diagnosed.
It's possible to be XO--that is, one X chromosome only. Those with this "monosomy X" are female. It's called Turner Syndrome and is accompanied by a higher rate of cardiovascular and kidney abnormalities, and delayed puberty and infertility. (Women who are mosaics, that is only some of their cells lack the second X, are generally less severely affected).
But even if you are "normal" XY or XX, you may not be typically male or female. For example, you may be XY chromosomally, but phenotypically (that is, in appearance) female, if you have complete androgen insensitivity syndrome. That means a mutation in the gene required to respond to the masculinization effects of testosterone. The "default state" is to develop as a female. This may not be diagnosed till puberty, when failure to mature leads to diagnosis. These women generally identify as straight females.
That's just one example. There are many others where sex or gender are ambiguous for a variety of reasons. There are many ways to be biologically intersexed, sometimes with physical features of both sexes. It used to be that doctors at birth would decide "which sex" they thought an intersexed child should be, often with disastrous consequences. Increasingly, parents and intersexed individuals are demanding the right to be left alone and decide on their own gender identity as they grow up. In many cases, empowered young people decline the invasive surgeries that would make them more "normal," but this isn't true for everyone.
A now discredited view suggested that absent sex organs, a boy could be successfully raised as a girl, which was used to justify many "sex reassignment" surgeries of intersex children. The most famous victim of this was David Reimer, whose penis was accidentally cut off at circumcision. His parents were encouraged to raise him as a girl, but he was never happy in that identity and when he learned the truth, reverted to being a male. He died of suicide, ultimately unable to resolve the conflict between how he was forced to live growing up with who he was. And revolting abuses still continue, notably regarding girls who might be.... "less feminine."
Given this diversity, it's not surprising that gender identity is not necessarily a strict binary. It's also not surprising that some people identify as transgendered; just from these few examples, we can see that there's a wide range of biological reasons that may lead to differences in how someone feels about themselves, versus how they are "plumbed".
Isn't it about time that we stopped trying to put labels on people and shove them into strict boxes?
To read this entire series in order, visit the Genetics Page.