treatment of people independent of gender

I had, for some reason, associated the Left with the concept of ‘Gender Neutrality’. Multiple recent experiences have shown me this was a faulty assumption. It became most clear with the massive negative feedback I got when questioning why, in ‘killed even the women and children’, it is still in modern day considered worse to kill a woman than a man. But there was a hint the Left is not actually associated with gender neutrality right before when the Trump administration had made military testing Gender Neutral (same test for everyone independent of gender). I was surprised that decision came from the Right and also surprised the massive opposition was by lefty lemmys.

I know some species of birds have the genders become very different from each other and some, like Vultures, have females and males that are nearly indistinguishable. It, after-the-fact, makes sense to me that Gender Neutrality (treatment of people independent of gender) is potentially a different thing from the ‘Gender Rights’ fought for by the Left. Anyway, so I have been awoken recently to Gender Neutrality not actually being of the Left, acceptable to the Right, and I am most curious in which ideology ‘Gender Neutrality’ is the accepted ‘correct’ view. So

Which ideology is associated with “Gender Neutrality”?

edit: I do now see how Gender Neutrality is the removal of gender distinctions whereas the ideal of the Left is chooseable gender distinctions.