How does language produce identities?

I have to disagree with the other answers. I think the evidence supports a yes (with a caution on the interpretation of the word "produce"). The way we speak to children and ask them to speak back contributes strongly to their gender identity. Having an available label such as "queer" can contribute to a particular kind of sexual identity. A better book to look by Lakoff is Moral Politics which is much less partisan.

But a better starting point is identity in general, rather than political identity. And identities are complex creatures. A great source of evidence for the processes involved are studies of bilingualism. There you can see where and how people use which language. I usually point people to the phenomenon of 'code switching' which often hints at language-based identities.

To address the objection of this being a "linguistics question". It is unless you assume a very modular view of language and identity. They are both complex, unstable and not easily bounded concepts. So as long as we keep that in mind, we can make interesting observations about their relationships.