It might turn out to be like this: There is no significant difference between matter and antimatter, except insofar as they are related to one another. A proton is attracted to antiproton, while each is repelled by its own kind. Our universe, as a contingent matter of fact, has more matter than antimatter. But, perhaps, if one swapped the matter and antimatter, the resulting universe wouldn't be different in any significant way. If we this is true, we might say that there is a relational matter-antimatter essentialism. It is of great importance to matter and to antimatter that they are matter and antimatter, respectively, but it is important only because of the relation between the two, not because of intrinsic differences.
I don't know if it's like that with matter and antimatter, but I do know that it's like that with the Father, the Son and the Holy Spirit. The only important non-contingent differences are those constituted by the relationships between them. (There are also contingent extrinsic differences.)
Could it be like that with men and women? The special relation between men and women--say, that man is for woman and woman for man, or that one of each is needed for procreation--is essential and important to men and women. But there are no important non-contingent intrinsic differences on this theory.
There might, however, be important contingent theological differences due to some symmetry-breaking contingent event or events. Maybe, when the Logos became one human being, the Logos had to become either a man or a woman. If the relation between men and women is important, the decision whether to become a man or to become a woman, might have been a kind of symmetry-breaking, with other differences in salvation history following on it. In itself, that decision could have been unimportant. If the Logos had become a woman, we would have a salvation history that was very much alike, except now Sarah would have been asked to sacrifice a daughter, we would have had an all-female priesthood, and so on.
Or perhaps the symmetry-breaking came from the contingent structure of our sinfulness. Perhaps the contingent fact that men tended to oppress women more than the other way around made it appropriate for the Logos to become a man, so as to provide the more sorely needed example of a man becoming the servant of all and sacrificing himself for all, and in turn followed the other differences.
I don't know if relational gender essentialism is the right picture. But it's a picture worth thinking about.