I have a disability that's about as visible as they come. I've got the powerchair, the involuntary movements, a cerebral palsy accent, the works. Rather understandably, the first thing you'll notice about me if we meet is my CP.
Yet, contrary to what many people are saying these days (primarily about race, like here and here), I love it when friends and colleagues say they don't see me as having a disability. Possibly the best comment to this effect that I've heard came from a long-time mentor who said, with reference to my powerchair, "I don't care how my employees get to work".
It's not that there's something wrong with these people's eyesight -- and even if there was, I've run over most of them enough times for them to notice that something was up. And it's not that they don't acknowledge that my disability sometimes causes difficulties. We talk about these things when they are relevant. It's that, as dramatically evidenced by the "invisible gorilla" experiment, seeing is a matter of attention. And my disability is low on my friends' lists of interesting and important things about me, just as it is on mine.
I am a human being, a scientist (specifically, an ecologist), a teacher and curriculum nerd, a rock climber, an atheist, a vegetarian, and a world federalist. I like science fiction, country music, kayaking, and learning Brazilian jiu jitsu. All these things are more interesting and, in various ways, closer to the core of who I am than the incidental fact of having had encephalitis at 4 months. Yes, my disability interacts with these identities in various ways, sometimes rather obviously. And yes, it sometimes affects my perspective on things. But it's incidental to the person I fundamentally am.
[EDIT: A paragraph that really should have been here to begin with]: My disability (like my gender, race, etc.) is entirely accidental. Therefore, it can't
be fundamental to who I am. If it was fundamental, it would mean that
who I was was determined by circumstances rather than the gradual
process of shaping myself into the person I want to be (in interaction
with my environment, of course). That would be abdicating a
responsibility that simply cannot be abdicated.
It's OK if you notice my disability. After all, it's pretty hard to miss. But after we've interacted for a while, I hope your attention shifts to other things. And if you say that you don't see me as disabled, I will conclude that you're seeing me as me.