Things that affect your way of life creep into your identity. Disabilities—including physical ones—change how you live, so they change how you view yourself and your relation to society (your identity). “A part of one’s identity” is maybe more fitting, but that’s pretty pedantic.

Also, I’m not sure you should suggest that someone’s identity is somehow less real than a mental condition. Both of them are integral functions of the mind that deeply and directly impact a person’s life. While I grant that many see identity as ‘less important’ or ‘more mutable’ (and thus less impactful) than diagnosable conditions, I’m not sure we should accept that without argument, and this comment inadvertently accepts it a priori.