Actually, in my experience left-wingers seem to have completely contradictory positions on that matter. For example, they claim that transgenderism is a veridical condition (a view which I share), a position that implies that gendered minds do in fact exist. nBut, i the very next sentence they will deny sexual dimorphism in human minds. It is a prima facia absurd position to hold, given well understood phenomena like the differential distribution of hormones and the effect of hormones on behavior. Of course, by "left-winger" I really mean left wing academics in subjects like cultural studies, (continental) philosophy, "theory" and "critical studies" etc.
I partly agree with that. For example, I have argued that if it is true that there is no sexual dimorphism in human minds, people with male sexual organs who claim to be women (and vice versa) are mistaken (e.g.,
http://rightlyconsidered.org/2016/10/14/jordan-peterson-and-the-pronoun-imperative/#comment-724 ). That would imply that usual left-wing beliefs on the matter are false.
However, that is not in conflict with the assessment that many (I'd say most) left-wingers agree that there is no sexual dimorphism in human minds. They do agree, but what they do not realize is that there is in some cases a contradiction between that view and some other views that they have. In some other cases, though, it's not clear that they contradict themselves, because sometimes they also take gender to be a social construct in some obscure way, and it's not clear what they believe the difference between transgender and non-transgender people is - or they think the difference is something not to do with male or female minds.
In any case, I do agree some of their views on these matters are untenable (though in my experience, even suggesting that the views might not be true will, in most left-leaning venues, result in immediate demonization, vilification, mischaracterization of one's intentions and beliefs, etc., by many people, so perhaps one needs to be cautious).
As for transgender people, the question is whether they are correct, which depends on things such as whether [some, all] transgender people with male sexual organs who claim to be women actually have female minds, or at least female parts of the mind that make the claim that they're women true, if there is such part - which I think is true as I understand the words, but there might be more usages.
It's a question for both scientific research and conceptual analysis. But one can tackle them at one's peril. More precisely, researchers might risk attacks that would hurt their careers if they end up finding something that is in conflict with some ideologies and saying what they found; conceptual analysis one can do on one's own and at no risk, but saying something tends to result in attacks from the left and/or from right, depending on what one says.