As a woman, I'm a little frustrated by this societal idea of what men vs women think about sex. There are women who tend to be promiscuous, or have high sex drives. There are men who don't. Culture tells us that women are supposed to be more easily chaste, but all that does is reinforce the pressure on women to be chaste, not actually tell us anything about the natural tendency towards wanting sex. And the evolutionary biology take on this tends to reflect this idea, rather than actual data.

In addition to this, I am attracted in that way to people I know and care about. I have had a number of different relationships over time, and what they look like has had actually very little impact on what I've been attracted to, regardless of any time of the month. I don't change what I look at over the month, I don't change how I feel towards my current partner based on it (in terms of whether I desire him because of his looks or his personality) either. Yes, women have fluctuations (to a degree, and it's more noticeable in some women than others) in how much they desire sex over the course of their cycle, but that doesn't really change anything about their overall desire for it or make much of a difference to the question OP is asking. Some women have high sexual drives and they have to stop themselves and struggle with their chastity just as much as any man, they just have society putting more pressure on them to do so.

Edit: As a male, I simply cannot relate to being attracted to Nice Guy Nate and Chiseled Chad in alternation based on phase of the moon.

Neither can I, and I'm a 27 year old woman. I've always been attracted physically, as far as that goes (which is not very far once I actually being the relationship process, since then I find out who they are and that's what really matters) to the same type of man, regardless of where I'm at in my cycle.