A bit of nuance to what you say there…

LGBT people say gender (not sex, gender) is a social construct because the evidence points to this. How gender has been expressed has varied wildly over recorded human history (from customs to clothes to behaviours to jobs to everything else). In any given point of history someone’s sex has been linked strongly to a particular gender expression, but the fact that those expressions vary deeply from culture to culture show they’re socially constructed rather than purely biologically determined.

When you say they think they’re not “important”, I think LGBT do think gender expression is important. What’s not important is squeezing into the two expressions that society traditionally had. Or welding yourself to society’s expectations based on what genatalia you have.

History (for the most part) had two distinct gender expressions corresponding to the two sexes. But this itself was heavily influenced by society being tightly coupled to the biological reality and differences between men and women. Women had babies. Men were stronger. The gender expressions followed from that and you had to stay in the one society expected because that’s what kept society functioning. Religion is a social construct that enforces this.

But as society has evolved we’re no longer bound to these distinctions in the same way and the gender fluidity of people - which has always been there - is now able to express itself in more variety.

There are people born male who are far more comfortable living in society’s ‘female’ behaviours and traits. And vice versa. There are men who are attracted to men and women to women. There are people born female who have deep seated psychological need for their body to be male. All these people have always existed it’s just in the past they got sidelined as ‘sinners’ or divergent because society basically consisted of childbearing and hard manual labour.