(sorry for the lengthy response...)
Biological essentialism sounds like 'evolutionary biology as a social construct' and nothing since has steered me away from that or clarified your position on that.
I guess this is the crux of the disagreement, which comes down to how we read the original text. I don't see it as ascribing a constructionist process to the field of evolutionary biology, and I definitely don't think the author is trying to say that organisms are evolving toward some ideal form. I do think that biology describes real things in a constructed/conditioned way, but that's not to say that the physical hardwiring of our bodies is socially constructed; and I don't think the author is trying to suggest that.
The author doesn't use the phrase "social construction," and we aren't working here with strict binaries. In other words, just because we reject something as essentialist, that doesn't mean we're beholden to calling it constructionist. It's not an ultimatum.
I see biological essentialism, when it comes to gender, as basically saying the following: that our gendered practices correspond to some internal essence or substance, and that this internal substance remains unaffected by social or environmental conditions. In such a model, evolution has a predetermined plan and is working toward the realization of that plan. Those who oppose transgender identification appeal to essentialism in order to make the claim that non-cisgender people are rejecting some natural order, and that doing so is harmful to themselves and to others.
The author is simply saying that this isn't the case, and that evolutionary biology doesn't support the idea of biological essentialism. We have bodies, and they're structured a certain way--but they aren't evolving toward some ideal form or essence, or approximating some optimal model. After all, environments change too; it doesn't make sense for organisms to be evolving toward some best possible solution.
If we reject this kind of biological essentialism (which is what I think the author is talking about), then it doesn't make sense to say that transgender subjects are denying any bodily essence. Of course, the problem with this position, which is also what the author is commenting on, is that we also can't permit transgender subjects to say they're identifying with some other kind of internal essence or substance--some metaphysical sense of self that is alternative to what biological essentialism would proclaim. The author is saying that our current mode of identity politics is still imbricated in the ideology of the metaphysical self, and this contradicts the arguments made against biological essentialism. It's an inconsistent set of practices, basically.
but the process of selection is a byproduct of environmental pressures, no?
In short, yes. I was simply objecting to where that pressure falls. I'm saying that environments don't have a direct impact on the kind of mutation that happens. To take the tuna example once again, it's not as though the environment intervenes with the genetic makeup of tuna-eating organisms and says "alright, time for a mutation so that these fellas can eat some shrimp instead!" Mutation just happens, and the environment directs selection ("directs" in the most non-intentional way, of course).