There are enough people, mostly on the left wing, who refuse to accept that we are born with different brains, that author Steven Pinker felt he had to write a book called The Blank Slate to refute this idea. In a famous example of blank slate thinking, a sex change clinic for children with ambiguous genitals here in Norway would randomly assign sexes to children, believing them to adapt to any sex assigned to them, since gender roles were obviously a construct of society, and male and female brains were of course identical at birth. It turned out to be disasterous for the children in question, and they changed their practices to include a gender identity test.
The way the Scandinavian system is designed is strongly biased toward this kind of thinking.
I should note that what Americans tend to call leftism isn't very leftist compared to what we have here in Scandinavia. Obama would not be considered a leftist, and even the populist right wingers in Scandinavia approve of universal healthcare, for example.
Based on what you've said so far, you're closer to a centrist/moderate than a left winger, on my scale, which probably extends much further left than any sensible American would reasonably want to be. Basically, the European (and especially the Scandinavian) scale of leftism begins where yours ends.
You can't please the gender rights faction of your leftist movement without accepting that genetics is completely insignificant, because if you do say it makes a difference, you might be taken to be a sexist, and perhaps even a bit of a racist, since different ethnicities have somewhat different genes. And once you do that, you must apply the same principle everywhere to remain logically consistent. And that's how you get the cloned mice.
I really don't know what to say about your statements about gender and race. They're really not applicable to my own experience with movements in my country.
Of course Obama is not a leftist. Far from it. His version of universal health care was a plan hatched by right wing think tanks and first implemented by a Republican governor.
I'm absolutely not a centrist, by any stretch of the imagination. I am an autonomist Marxist.