This is a question I've been getting a fair amount lately, and I think it's worth exploring. Let's dive in, shall we?
Intersex activists, in general, are fighting for the following:
1) Awareness of what intersex is, what it is not, and that intersex individuals exist.
2) Understanding that intersex bodies are healthy, natural, normal bodies that don't need "fixing." Intersex is thus not a medical issue, and shouldn't be treated like one.
3) Intersex individuals must have a right to consent to anything done to their own bodies, especially since such "treatment" is not for medical/health purposes. No one else - whether guardians and/or clinicans - can truly consent for each intersex individual. (So, for example, there's no argument that an infant that needs a heart transplant shouldn't get one because that infant doesn't understand what a heart is, or the complications involved in transplant surgery. On the other hand, an individual doesn't incur any health risks if their clitoris is enlarged, or if they happen to have a vulva and XY chromosomes. These aren't medical concerns, and therefore don't require medical treatment.)
4) Intersex individuals are normal people, even if we possess less typical suites of biological traits. The only reason these suites are considered atypical is because they aren't so easily shoehorned into one of two acceptable bodily forms - "male" or "female." They still fit into the normal ranges of human biological variation. Thus, intersex individuals' bodies shouldn't be shamed, fetishized, and exploited.
5) The shame, stigmatization, isolation, and trauma many intersex individuals feel result from medical "treatment," and not from knowledge of one's intersex. One must stop such treatment in order to end lasting emotional and psychological harm.
6) Intersex people shouldn't shut up and eat their shame. Intersex individuals are prevented from connecting with one another, and from decrying abuses against them by the medical community because we're told that one's intersex is a personal issue that shouldn't be discussed for fear of being shamed. Really, our shame comes from being told, whether directly or indirectly, that our conditions are shameful; conversely, reaching out and advocating for ourselves would allow us to empower ourselves and generate change. Our voices need to be heard and not silenced.
7) Intersex doesn't necessarily have anything to do with one's gender identity, gender role (including presentation and performance), sexual orientation, sexual behavior, or anything other sex-and-gender variables. Intersex is biological in nature, even though it's considered a social emergency, because some individuals expect that based on one's sex, all those other variables have to line up in a particular way according to "male" or "female" standards. Even if some of these other variables are at least partially informed by biology, you can't make predictions about how someone will identify with regards to any of them just by knowing that they're intersex. (Really, you can't do this for anyone, whether they're intersex or not.) After all, lots of people who are not intersex identify in ways that are considered not to "match up" to other aspects of themselves (e.g., a male-identified person that wears skirts).
It's important to note that not all activists are fighting for the same things, though. Many activists would add a 8th condition:
8) Repealing the use of "disorders of sexual development (DSD)" as a replacement for "intersex." While the term "intersex" itself is problematic, and some have no issues with changing it to something else (as I've previously posted), DSD is a poor choice for several reasons. DSD really came into being through ONE intersex person (Cheryl Chase) working with medical doctors and academics (notably, Alice Dreger). Can one intersex individual speak for how all intersex individuals wish to identify? Likewise, can an outside group (here, the medical community) determine how another group must identify, even if it's not how that group prefers to identify themselves? I would strongly argue no to both questions. DSD is also a term that falls in step with how other medical jargon sounds ("So science-y!"), further reinforcing the flawed view that intersex is a medical condition requiring treatment. (As well as allowing for eugenics. Some estimate that as methods of pre-natal screening become cheaper, less invasive, and more accurate, it may be more common to "diagnose intersex" and subsequently abort fetuses simply for being intersex.) Furthermore, DSD is not able to be used as an identity; one can identify as intersex, but one would be very hesitant to identify as a "disorder," which absolutely carries negative connotations in English. Hida Viloria states that in other languages, translations of "disorders of sexual development" misrepresent intersex as transgender or having a queer sexual orientation or something non-intuitive and confusing, which simply violates the first objective of intersex activists. You can read more about DSD here.
Not all intersex activists are on board with repealing DSD, however. Some individuals that have worked closely with Chase and ISNA in its earlier, progressive days feel ambivalence about the term, or feel that since some parents and doctors like DSD, that using it is okay. I would definitely question, though, whether this term has gained widespread support among intersex individuals themselves, and if not, whether using it is still acceptable. I would also question if those intersex individuals supporting it do so because they have inherently always felt that their bodies are disordered and need fixing without outside influence, or whether they feel this way because of the shame induced by clinicians, parents, and mainstream society at large.
It's also important to note that not all intersex individuals are supportive of what intersex activists are fighting for. Many individuals view their intersex as a medical "condition," as it was very very very likely described to them by the medical community. Those that have never been exposed to alternative perspectives may never have questioned whether intersex is truly medical in nature, and whether it is ethical to alter one's body without consent if such alterations are not medically necessary. Some intersex individuals feel an affinity with the queer community, even if they don't identify as queer themselves, because queer activism targets attempts to repress autonomy based on perceptions of what they are supposed to be and do with their bodies - something in line with intersex activism. Others don't want to have any involvement with queer communities, and greatly oppose inclusion, as I've posted previously.
Finally, it's important to note that activists not engaged in intersex activism may confuse the efforts of intersex activists with other movements'. For example, some assume that all intersex activists want to repeal sex-and-gender binaries for good. I am all for allowing for full sex-and-gender expression, whether individuals wish to use traditional "female" or "male" identifiers, or with other more complex, fluid, and non-static identities. However, I do not advocate for these goals specifically as an intersex activist because right now, the immediate concern must be ending harmful "treatment" practices that cause psychological, emotional, and even *actual* health problems (!) for intersex individuals. Other individuals are going to be less receptive to questioning the utility of the sex-and-gender binary, and how well it actually resonates with others' lived experiences than they will be to simply consider whether it's ethical to poke, prod, and lop off parts of healthy bodies without consent. If we tried to go from that angle, we'd probably be waiting much much longer to end the very immediate, very real trauma intersex individuals are undergoing now. Focusing on the human rights issues at hand are where our priorities must lie, regardless of whether intersex activists ALSO support others' expression of their sex and gender identities.
So, despite the fact that there isn't total consensus, there are a lot of things intersex activists are collectively fighting for. Let's work toward meeting intersex individuals' needs, thus gaining equal rights soon.