Although, this is somewhat causal in semantics regarding a scientific topic, I think this is a good way of helping people understand a bit better:
So, we have the common biological binary of XX and XY, and then we have the occasional XXY. These chromosomal standards aren't definitive, though. They are only blueprints. There can be XX males and XY females. The reason for this is because gender is a neurological matter. The fetus doesn't develop everything in a single go; there are two phases: the physiological and the neurological.
Neurology is still a biological factor, though, so the brain will still develop somewhere between masculine and feminine. But the brain is an immensely complex organ. Nothing is ever black-and-white.
However the brain develops, it isn't definitive of anything, either. It only sets the framework for one's mind/consciousness, and that is where gender manifests. That is why gender can be variant beyond male or female. Some can feel one or the other no matter what their physiology is or their chromosomes. Some can feel as if they're both, or fluid between the two, or even neither. That "feeling" comes from our particular wiring, and is really more of a knowing, because it's a deeper sense of self than just some fleeting emotion.
Many believe that gender is wholly a social construct, but that's only part of it. Gender definitely comes from our hard-wiring, but being an intelligent species with greater self-awareness allows us to interpret those signals uniquely. How we navigate that sense of self in our environment is the 'social construct' part of it.
So, it really is foolish to believe that sex and gender are mutually exclusive. It's just not the way it works. All anyone has to do is research sex determination, SRY expression and non-disjunction, and how these aspects of human development relate (and don't relate) to gender identity.
Of course, it's so much easier to just reduce everything down to penises and vaginas, but that opinion is one of social bias and lack of education, particularly in those subjects mentioned above.
No Layman's opinions nor any religious beliefs can outweigh scientific scrutiny, no matter how much conviction is involved. Apparently, though, we're living in an era of religious totalitarianism; where science is the handiwork of Satan, and anything that isn't in line with the infallible, Republican word of God is a dark, homosexual, transexual, feminist agenda.
My agenda is just to love and be loved, to enjoy life the best that I can, to write my heart out, and to hopefully make a positive difference in someone's life. I do my best with what I know, and I never claim to be 100% right. Maybe it can sound that way with how passionate I can get, but that's just the nature of philosophical thought.
I don't know why it's so hard for some people to just live and let live. It shouldn't even matter to anyone why anyone else identifies differently. People who take on that attitude miss out on some great friendships, or business connections, all because they choose to believe terrible things about someone they don't even know. It's such a shame.