The reason for grouping sexuality and gender identity together wrt civil rights
I wrote this a few days ago at Slacktivist in response to someone who didn't understand why T was grouped with LGB in LGBT since the LGB is about sexual orientation and the T is about gender identity. Person said it had always seemed arbitrary.
It's not actually arbitrary. It's about traditional gender roles. (Those will likely never stop fucking up the world.)
The traditional model is this: Sex determines gender, gender determines attraction.
Intersex people are considered broken because they lack a clear biological sex at birth (hence traditionally surgically assigning them one at birth.)
Trans* people are considered broken because they don't let biological sex determine gender. Unlike intersex people this is usually (though not always) seen as a choice and thus fundamentally immoral.
Non-straight people are considered broken because they don't let their gender determine their sexuality. Unlike intersex people this is usually (though not always) seen as a choice and thus fundamentally immoral.
Sex → Gender → Sexuality is the model that says these groups are all wrong. Sometimes that wrongness is seen as a problem to be cured, sometimes it's seen as an immorality to be opposed, but something is wrong and must be fixed.
Try to dismantle that model and everybody under the umbrella benefits, try to enforce it and everybody under the umbrella suffers.
That's why they're grouped together: the same thing is keeping them down.
It's similar to "people of color" in that what they have in common isn't that they're the same, far from it, but that racism is keeping them down.
Of course there are a lot of people who want to dismantle only part of the model. The trans* people that Shiftercat mentions [who thought being non-straight was a mental illness] were fine with the idea that gender ought to determine sexuality. If you want additional depressing examples read the opposite viewpoint too.
It's not hard to find a plethora of articles from lesbians who think that transwomen are men that are trying to exploit a loophole in order to fuck lesbians. (Because ... you know what, I can't even come up with a sarcastic way that that makes sense.) Those particular lesbians are very opposed to the idea that gender determines sexuality, but very in favor of the idea that sex determines gender.
Or note that both groups I just mentioned write on the implicit assumption that intersex people either don't exist or are unworthy of a place in a cohesive worldview.
Or read the writings of intersex people who think that anyone who isn't intersex that doesn't identify as a straight member of the gender associated with their birth sex is stealing intersex people's identity (only they get to claim a say in the matter because only they have biological ambiguity at birth.)
All sides have definitely been against each other, and members of them continue to be, but sex, gender, and sexuality are all linked by a worldview that seeks to keep down anyone who violates the idea that your gender ought to be your sex at birth (and you ought to have a clear sex at birth) and your sexuality ought to be determined by your gender (you ought to be attracted to be the people of the opposite gender.)