Does the existence of intersex people invalidate the binary conception of gender
You ask a complicated question very simply! Here's some advice about how to pursue this topic, with a few oversimplifications of my own. Sex (physical sex) is often distinguished from gender (gender identification in people, often culturally influenced) as well as from sexuality (sexual orientation). Intersex people have bodies that are not "typically male bodies" or "typically female bodies" but have elements of both. This ranges from (controversially) hypospadias in men (the urethra not opening at the tip of the penis) to individuals with both an ovary and a testis. Anne Fausto-Sterling's excellent book Sexing the Body describes the range. Then the question is, do we regard intersex individuals as "abnormalities," and thereby preserve our traditional understanding of biological sex as a binary, or do we regard intersex individuals as counterexamples to our traditional understanding of biological sex? Some (including Fausto-Sterling) appear to think that the answer to this depends at least in part on the prevalence of intersex persons. I prefer the approach of Joan Roughgarden Evolution's Rainbow, who explores the biological significance of sex and its variability across the plant and animal kingdom. I think she shows that are biological reasons (from evolutionary considerations etc) for giving up the binary conception of gender.
(Intersex should be distinguished from "transsex" in which individuals have sex typical bodies but different gender identity. Both should be distinguished from sexual orientation.)