Intersex conditions are disorders of physical sex development, and the specific disorders themselves most of the time sex-specific. It is a physical medical condition, and they certainly do not create a spectrum of sex: There is not a third or an inbetween kind of breeding setup, just bugs in building the proper things. Bugs that are insanely rare.

Women with more male-like personality goes into that "variation in a shared system that has sex-linked distributions": There are women that have more typically male personality configurations and the reverse, just as there are tall and short people. Nothing surprising about that, and it doesn't relate to sex itself being a binary dictated by two different reproductive mechanisms.

Sorry, you are falling for a category system that is entirely human-made. Nature doesn't care about "disorders" but produces the whole spectrum. Nature doesn't even care about that the evolutionary fitness of many variations is zero.