This has traditionally been a very divisive point within radical feminism, and it typically divides the discussion into transphobic social-constructionist radical feminists (like the source of my original infographic) and neo-essentialist post-feminists.

Personally, I came to radical (pro-)feminism from the feminism mainstream within anarchist culture, which is more pro-transgenderism (and therefore essentialist), and I haven't fully came to a conclusion on this specific issue. It doesn't help that neither of the two sides really care much for empiricism (outside of horrible "look at this fMRI" type stuff).

A comrade of mine told me that these are good articles on this topic, and while I haven't yet read them, I know the author to be very good at getting that comrade (who is more tumblr-feminist third-wave-y) and I to agree, so they probably would clarify my position on this and maybe yours:

• https://radtransfem.wordpress.com/2012/02/03/sex-educations-gendering-and-regendering-women/
• https://radtransfem.wordpress.com/2011/12/12/genderternary-transmisogyny/

Edit: It's annoying that less wrong's reddit instance doesn't hyperlink raw links, but I dislike hiding what I'm linking to, so... sorry if you're too lazy to cut and paste, I suppose.