[socialismisok]

It's important to remember we're discussing the margins. The XX, XY definition is functionally good enough for nearly all cases.

But there exist people whose sex doesn't work into that model.

Consider some 46 XX intersex people. In these cases, outside conditions (typically an endocrine imbalance in the mother) leads to the development of a penis, and the loss of a vagina. These children may be raised as boys. Similarly, some XY people are born with autosomal defects that prevent them from effectively processing testosterone into dihydrotestosterone. As a result, their bodies develop into what we would consider typically female. They are often raised as girls.

There are dozens of conditions similar to these.

"XX male syndrome" might be one example of specifically what you are looking for - people who are scientifically discussed as male despite having XX chromosomes, a typically female karotype. It can be caused by autosomal origins

Ultimately, we cannot remove the discussion of sociological science from biology, because we make choices for kids in these cases. And those choices differ depending on culture. The US preferentially gives intersex people male gender, while Saudi Arabia does the opposite, even for the same conditions. In this way, even biological sex has some social component.