An intersex person has anatomical traits of both female and male. Their genes, reproductive system, genitalia, and/or external appearance partially resemble the female and partially the male. These traits exist naturally, usually with a genetic cause. While ambiguously shaped genitals are best known, there are many diverse intersex conditions. "Intersex" (like "transgender") is an umbrella describing any physical abnormalities that do not conform to traditional concepts of female bodies and male bodies.
What transgender is to gender, intersex is to sex. Just as sex and gender are not the same, transgender and intersex are not the same. While some intersex people identify as trans, most do not. Because transgenderism has neither been confirmed nor denied as biological in origin, it is unknown whether we can truly categorize transgenderism as an intersex condition or not. Trans people need to realize there is some tension between the two groups because trans people have been too quick to equate, rather than relate, intersex ideas with transgender ideas. We should take care to understand our overlap and acknowledge our differences.
Nevertheless, intersex and trans people are common allies in a struggle against the worldview of the gender binary where sex is equivalent to gender and any violation of the sex/gender binary is sin. The existence of intersex people is an attack by Nature herself on the sex/gender Binary. Here's a rundown:
Intersex Stories - Personal stories of intersex Christians
Intersexuality and Scripture - Analysis of what Scripture applies to intersex people and conditions
What Is Sex Exactly? - Intersex, and post-ops complicate the definitions of "female" and "male" so I go exploring.
The challenge of intersex conditions for theology - Quote: Christ himself has a wounded body even after his resurrection. God inhabits unexpected, non-dominant bodies. . . . Jesus invites people to touch his wounds, for this speaks of helping people to overcome their fear of coming into contact with “distorted” bodies."
There are many, many intersex support groups. Like transgender groups, they need not be religious in nature to be helpful. The Intersex Socity of North America, for one. Listing all of them would be overwhelming and not that helpful. Here are just the most relevant organizations:
Intersex Support Group International - A Christian organization advocating intersex awareness and rights within the Church.
Organization Intersex International - Includes many Christian and transgender articles
Objection: Christ and the Bride - including intersex criticism