If someone is intersexual and is comfortable with that identity they should be allowed to choose that identity. Just because someone has ambiguous genitalia does not mean they are going to want that 'corrected'. Let them decide when they are older, and if they are comfortable as they are born then that's fine.
Intersexual people should be permitted to select the gender with which they want to identify with when they are intellectually capable of making that decision. This is because of the fact that many people feel as if they were born into the wrong sex. Allowing these people to choose the sex that they identify with eases their transition.
Gender is a main way that people identify and are comfortable with themselves so forcing someone to be something that they do not believe they are would be emotionally devestating to nearly anyone. Therefore, for the sake of their own sanity in an already troubled life, we should allow them this luxury so that they can have some comfort.
Intersex individuals should without question be able to decide which gender they identify with. No one else is able to determine which gender they should identify with. From a medical standpoint, and even a religious one for those that are religious, there is no question they have the physical parts of both. The way they feel and identify is the only way to really determine it.
I do not think that intersexuals should be permitted to select what gender they want to identify with. I think that such a tactic would just be something that would be more of an opinion rather than a medical clearance. I think that such issues are being manipulated by political bias.
This outlines a pretty robust explanation of what it is to be intersex, and how it varies.
This ranges from people being born with both sets of genitalia, to people being born with malformed or ambiguous genitals.
Under this idea, a great many of these cases are actually identifiable as male or female, and simply have some body abnormalities akin to a person being born with fewer or more fingers. In those cases, you would think there would be no real advantage to gender selection, as things are abnormal, but still clearly male or female.
In other cases, where a person is born with genetics that are male, but a body that presents as female, reacts as female for the most part, and the person doesn't even recognize that there is any distinction.
Part of me sees it as a personal choice, as with trans individuals, to identify as male or female. Part of me doesn't think a person should try to push themselves into a particular box in this regard. As with most of these things, I think we need a lot more study, and a lot less grandstanding, to figure out the best fit, based on the best medical science.