I think the dishonesty is slowly coming to light.
I think you may very well be right. And the dishonesty emanating from the TRA position is evident in the wilful obfucscation - or in many cases I suspect woeful ignorance - as to what 'biological essentialism' actually means. I note that term has inevitably made an appearance on this thread.
Biological essentialism does not mean the recognition that humans are a dimorphic species, that we all have a sexed body, and that this sexed body falls into one of only two two available categories (including people with DSDs). That's physical biology. If your body doesn't function in the way it's designed to do: ie around the production of either small or large gametes - then you are atypical. I say this as a woman who has encountered infertility. It doesn't mean I'm not just as much a woman as the next female. My body is still designed around the production of large gametes - whether or not those, or my reproductive system, is functioning as it typically would. I'm a woman. I am not a third sex; people with DSDs are also not a third sex (or intersex).
Essentialism, on the other hand, means the theory that aside from the organic body there is some essence of what it means to be human - hence the name 'essentialism'. Philosophers have chewed the fat over this one since the year dot. For Descartes it fell into the reckoning of a body/mind dualism, in the enlightenment it varied around the theme of the human capacity to reason; for theologians it was the idea of an immortal soul that could live on after physical death. Humans have always railed against the idea that we are nothing but bodies: it seems somehow to be the essence of the obscene.
In gendered terms, essentialism was an idea that particular social qualities are innately female. I.e. women are 'natural' carers and nurturers, we are child-rearers, our job is to maintain the home, we get 'hysterical' if we try to enter the economic marketplace and deny our natural function as wives, carers and mothers. Anti suffragists - ie Almroth Wright, argued exactly these points against women having the vote. And this is what is meant by ideology - a preconceived idea that's drip-fed into us from such an early age that in our minds it becomes fixed and immovable fact. Note how often such ideas rely on assumptions of 'well, that's just common sense', or 'that's natural/unnatural'. It's when we try to unpick it that we realise these are in fact not sensible propositions, and it's not natural but socially constructed. Being a home maker, for eg., is not irrevocably tied to having a female, sexed body.
This was where the theory of social constructivism came in. It was the polar opposite of essentialism - and gender essentialism is the idea that there's a core or essence of how women or men think, feel, behave, and present in terms of their appearance, gestures, dress, and stereotypical behaviour. This is the idea encompassed by regressive gender ideology, and to which gender critical people are completely opposed.
It means 'essence'. It's a mechanism of social control. It's not about organic bodies. And any TRA who tells you your GC position is 'essentialist' is showing their ignorance, and telling you that they don't have the first clue what they're talking about.