I have basically only been around TONS of umbrella cockatoo, Mollucans, Goffins, and Sulfur crested. I have only been around 1 RB2 and 1 MM2. The RB2 was a male, black eyes, and the MM2 was a female and I believe her eyes were brown (she is 15+)
I have to say that the goffins did not have red eyes in the female sex, and no M2 I have ever seen has had red eyes and I have been around both sexes. For instance, Beeba our M2 is not DNA'd but thats not needed as she lays eggs bi-annually. and Beeba is 18
HOWEVER I have seen some of SC2 that have red/brown eyes(and they were female), and I know all the female U2s I have seen have red eyes. (And that female U2s are WAY DIFFERENT in everything about them, their stance, body language, vocalization and the mental connection I got). I'm sure other cockatoos are just like that, although I have to admit I typically just stick around the U2s and G2s.
About U2's and their red eyes. This is the only species I have seen to have RED EYES (In females) from the time they are being very young. By the time they are about 3-4 months of age, their eyes are like their siblings brothers(dark brown/black), and they stay that way until 3years of age and up to sexual maturity.