There are commonalities between transgender and intersex experience. However, most people with intersex conditions do not identify as transgender--or even as intersexual.
Generally speaking, intersex is not an identity category. While some intersex people do reclaim "intersex" as part of their identity, most regard it as a medical condition, or just a unique physical state. Most intersex people identify and live as ordinary men and women... (Intersex Initiative)
Raven Kaldera is a transgendered intersex activist with congenital adrenal hyperplasia (CAH).
Emi Koyama has written extensively about the intersections between intersex and queer politics. Some excerpts are offered here:
[Intersex] [a]ctivists oppose non-consensual genital "normalizing" surgeries on intersex children primarily because they are harmful physically, emotionally and sexually, and not necessarily because they might get the gender of the child "wrong." ~ Emi Koyama
To list "intersex" along with "male" and "female" gives the false impression that one cannot be male or female if she or he has an intersex condition. This hurts people with intersex conditions who identify as male or female, and mis-educates the general public. ~ Emi Koyama
...there is already a lot of conflation between LGBT and intersex in the society, and constantly being combined with LGBT might prevent intersex from getting its own visibility, or make it hard for intersex people to find intersex-specific resources. ~ Emi Koyama
Adding "intersex" to an LGBT group must mean a commitment to take concrete actions to address the specific needs of intersex people; anything less is tokenism, or a mere fashion statement, which will not benefit the intersex movement. ~ Emi Koyama
Some relevant writings by Emi Koyama:
Aidan Dunn is an intersex and transgender activist. In this video, he discusses the way intersex conditions are romanticized and appropriated by transgender people.
Why is the idea of having an intersex condition so appealing to trans folks? Intersex is not glamorous. People with intersex conditions often face many horrific medical interventions. An intersex diagnosis would not make gender transition any easier. ~ Aidan
Eli speaks about the challenges of moving through the world as a person with an intersex identity.
I don't want to be tagged on to the end of the queer acronym.
~ Eli