This is something I have been studying and thinking about for a number of years. I am going to start with a little science on the effect of testosterone on gender specific fetal development and gender identity. The reason why is that is where I started and understanding what modern science tells us about the development of gender identity is going to be crucial to compare against what Jesus is saying in the scripture when I move on to that.
What modern science tells us about fetal development and gender is it is determined by exposure to testosterone in the womb. All fetuses essentially start out as female. For example very early on male fetuses develop a proto-vagina. Then about the middle to the end of the second month of pregnancy the mothers body will flood the womb with testosterone which forces the fetus to develop as male.
How much testosterone a fetus receives will determine how masculine the baby is, both physically and mentally. This applies to both genders by the way. If the fetus receives a lot of testosterone it causes skeletal changes. In the hands the ring finger will be longer than the index finger. In the face the brow ridge will be more pronounced and the jawline widens. Mentally the testosterone causes the brain to rewire itself as masculine.
If the fetus doesn't get much testosterone then it won't be as masculine mentally or physically. This is why some transgenders can look extremely feminine without undergoing FFS. You can read more about all this here.
http://www.livescience.com/18484-finger-length-masculine-faces.html Now the religious aspects. "Religious scholars" tell us that there were no transgenders in the Bible, which is technically true, but only because the term transgender wasn't created until the nineteen fifties. But there were emasculate men described in the Bible who they typically described as being castrated or eunuchs.
Something that I think is crucial to bear in mind when considering interpretations of scripture is the vocabulary they had 2000 years ago was much more limited than it is today, so words could have been used much more broadly. Today we have a much greater vocabulary and can more precisely describe a wide range of gender expression and definitions can change over time. For example, today a eunuch is someone who has been castrated, both of those are very literal terms and they have clearly defined implications. In biblical times the term eunuch was not exclusively used to describe someone who was castrated. Much like how today emasculate could be used to describe someone who has been physically castrated, a eunuch could be someone who simply isn't very masculine or even effeminate, so it is less literal and can cover a wider range of behavior.
For those reasons I think that when you read scripture which is thousands of years old you need to be careful to not take some things too literally. Another factor is interpreter bias. An interpreter may choose a term which has a very literal interpretation if it supports their bias. Another issue is there are so many different versions of the bible out now and they can have very different ways of presenting various passages.
So the passage that really got me thinking about what exactly was Jesus trying to say is Matthew 19:12. The first version I read was worded: Some men are castrate because someone castrated them, some men are castrate because they choose to be and some men are castrate because they were born that way, if you can accept that then you should. The way this has traditionally been interpreted is Jesus wanted his followers to be castrated. In fact there was a Christian sect where all the men followed that interpretation, but it eventually died out because they had nobody to keep it going. It might also be interpreted that way to tie it into the church doctrine of the celibate Jesus.
If we substitute emasculate for the more literal castrate it expands the possible interpretations. Written this way "Some men are emasculate because they were born that way" it doesn't necessarily mean that they were born without testicles. It could relate to behavior, which is something that we see. Some children express transgender behavior at a very young age, as toddlers even. I think it shows that Jesus understood that gender identity is something people are born with. So then when he says if you can accept it you should, I think what he means is if you can accept what he is saying, that some people are like that because they are born that way, then you should show them acceptance.
I could be wrong in my interpretation but, I think my interpretation is much more consistent with Jesus as a teacher of love, tolerance and acceptance, towards people who are often marginalized and shunned by the rest of society like they are lepers. In my interpretation he is making an observation of brain gender that is consistent with modern science. It may be my bias but I like a Jesus who is loving, tolerant, accepting, insightful and way ahead of his time.
A huge implication of Jesus saying people are like that because they are born that way is that it is the decision of God, if you are going to be prejudiced against someone for being the way God made them then you are questioning the wisdom of God.
I think the accepted church interpretation that Jesus wanted his followers castrated makes Jesus appear to be a nutter. It also goes against Jewish tradition, because in Deuteronomy it says that a castrated man cannot enter the kingdom of heaven. So it has Jesus preaching a heresy. He couldn't build his church on a community of eunuchs and when a sect did try it the sect died out. The doctrine of the celibate Jesus is also part of the church doctrine that Mary Magdalene was a prostitute instead of Jesus disciple. That doctrine has been looking increasingly unlikely ever since the discovery of the gnostic bible at Nag Hamadi which gave us the Gospel of Mary Magdalene.