Now I'm not asking for ethical apologetics but more of a scientific or creationist/Genesis explanation on their existence and how it coincides with the Bible. God created Male and Female only, and yet intersex people exist who have bodies with features that are both male and female. How can we explain this from a Biblical perspective?
Young Earth Creationists (and most other Christians really) teach that the entry of sin into the universe has many more consequences than just the moral corruption of people. The world is now in a permanent state of being increasingly run down, things breaking and falling apart, forever becoming less like the "very good" of the original created order.
So in regard to people, the fertilisation of eggs can mistakenly include the wrong number of chromosomes, resulting in genetic intersex conditions. An embryo can also, whether for genetic reasons or just through other mistakes in development, then have errors in its development, resulting in genitalia that do not match the genetic sex, or genitalia that combine features of both. Or it may only be at puberty that intersex characteristics will become visible.
Although much more unusual, there is ultimately little more theological significance to intersex than there is for other genetic corruptions such as those causing colour-blindness, nor compared to physical development problems like a cleft palate. The biggest theological issue would be that we need pastoral sensitivity when discussing things like gender, roles in the church, and relationships and marriage.
It appears to me that intersex conditions are explained in Christianity like any other birth defect. There is sin and suffering in this world, and from that comes unfortunate birth defects. God gave us free will to choose to love him or not. Falling from his grace and guidance will mean things like polluting the air we breathe, the water we drink, and the food we eat. A parent that falls victim to gene altering pollution can give birth to a deformed child, having done nothing wrong themselves.
Should a child be born with a deformity that child should be loved, cared for, and the parents and community should do what they can to allow this person to have a long, healthy, productive, and fulfilling life. If possible the ability for this person to be a parent should be preserved. Being intersex does not necessarily mean one is sterile. Mild forms of intersex may bring deformities that do not interfere with one's ability to have children but may bring a physical appearance that is inconsistent with a healthy male or female.
Christianity frowns upon a person dressing and acting like someone of the opposite sex. A person with complete androgen insensitivity will have XY chromosomes but because the body cannot process androgens, male sex hormones, the person will appear like a healthy female unless one looks close enough at the sex organs or DNA. Is this person a female in the eyes of God? We can only assume so. How is this explained? God acts in mysterious ways and this person's inability to have children should not be considered punishment for some sin. A person that has all the appearances of a female, and the natural desires of a female, should not be considered sinful for wanting to dress like a female and seek the companionship of a male because of her Y chromosome.
I do not recall the Bible having anything to say about intersex conditions. The Bible did have some things to say about men sharing a bed with another man, cross dressing, and about women unable to conceive a child. If the sex of a child is truly ambiguous then the parents and medical advisors will have to choose a sex for the child to be raised. If the child grows to desire to live as the opposite sex later in life then that can be explained by God's actions, sinful actions, or an innocent mistake made by those that cared for the child. Again this sin that causes birth defects may not be from sinful actions of the parents, it can be explained by original sin.
As God created man and woman in his image it is by following him that intersex people should seek to become the best man or woman they can be. The existence of intersex people does not mean there's 52 genders. It means that there is sin in this world. I mention the fact that there are only 2 sexes because it has been a tactic of some to use deformities of sex organs at birth as justifications for creating the lie of there being more than just male and female. People born without genitalia doesn't negate the male and female binary any more than someone born without arms means lacking arms is a healthy state to be in.
Some people are just born as eunuchs.
Jesus off-handedly addresses this when discussing divorce and sexual abstinence.
Jesus replied, “Moses permitted you to divorce your wives because of your hardness of heart; but it was not this way from the beginning. Now I tell you that whoever divorces his wife, except for sexual immorality, and marries another woman, commits adultery.”
His disciples said to Him, “If this is the case between a man and his wife, it is better not to marry.”
“Not everyone can accept this word,” He replied, “but only those to whom it has been given. For there are eunuchs who were born that way; others were made that way by men; and still others live like eunuchs for the sake of the kingdom of heaven. The one who can accept this should accept it.”
In particular, we're looking at this segment of Jesus's speech:
For there are eunuchs who were born that way;
In that statement, he's talking about what we now call "intersex" individuals. Some people are born without working sex organs, and that's fine. They won't be able to marry or have sex the way most people can, just like eunuchs who were made that way by men, but that's fine. Staying single and sexually abstinent is just as good in God's eyes as getting married and having sex.