Might this be Geneshaft (2001)...?
In the 21st century mankind was on the brink of destruction. Through genetic engineering however they eradicated such feelings as love and the desire for power. Since women are naturally less aggressive than men, women to man ratio was set to 9:1. Now people are engineered to have skills that others view as being necessary. There is a giant ring that now orbits the earth, that sits there and relays information back to an alien race that sent it. Now a team of five women will try to eradicate the alien threat.
The second episode features some type of mecha being released from a spaceship, and piloted by a team of women sitting in the bridge of said spaceship. They specifically talk about having to use an out-of-date version of the mecha's program, since the program wasn't scheduled for completion for another month.
The main character, Mika Seido, has reddish-brown hair, and appears to fit the description of being "rebellious," since she gets up from her seat and punches a male character in this episode.
The Wikipedia page for the show also describes Mika as possessing a white genetype:
Mika is the main protagonist of the story. She is short but has considerable strength, though it is explained that she has the genetype white, leading to her being mocked by other characters as being inferior. Mika is much more passionate and aggressive than many of the people around her, but is also extremely loyal. Mika was very close to her "mother," the woman who genetically engineered her, and her sentient dog. Her friend Ryoko was killed in the previous year, and she blames Amagiwa for her death, believing that he murdered her to save his own life (although since in this society humans are considered to be nothing more than the sum of their genes, Ryoko's death would never be considered murder since she had an identical twin). She repeatedly threatens him because of this, but finds it bewildering that he is so confident in her potential and abilities, especially since she is a "white." Mika eventually teams up with Amagiwa and helps defeat Mir and Sneak. She also finds that she has fallen in love with her former enemy.