Do female victims of rape have an increased risk of becoming a sex offender? It's said that men who are molested as children often become molestors when they get older. Is the same true of women who are raped? Is a female victim of rape more likely to become sexually warped in some way, e.g. initiating incest, pursuing children, dressing "slutty", protecting someone who molests children?

I figure if it's true that male victims of sexual assault often become predators, then it's likely true of female victims of sexual assault as well. The victims become the victimizers.
Our social constructs play a big role in influencing how we respond. As with most common cognitive mechanisms - confluence of environmental triggers meet a biological predisposition. 

Regarding belief systems: in many traditions, femininity is guarded due to its relationship to motherhood. Women are thought not to be sexual. Masculinity is sexualized in a different manner, which perpetuates violence against women as well as the association of masculinity to aggression. Women who have been abused may not become aggressors- but instead are re-victimized. The idea that they will protect a perpetrator like a boyfriend or husband is a coping mechanism of sorts. On a cognitive level it is a fear-based response.The response is different for men and women due to evolutionary traits as well as learned behavior.

Many people experience sexual trauma and are not warped or broken or damaged, in part because their learned behavior is based on a positive role model who has taught proper coping mechanisms which increase protective factors.  

I do believe, as a survivor of sexual violence myself, that there is a tendency to want to re-appropriate one's own sexuality and also to engage in a process of externalization through sexual experience and behavior in a way that might be labeled as deviant by others. Sometimes people respond by presenting as less feminine or less masculine as a way to distance oneself from the sexualization of their gender in order to feel safe. Sometimes people may respond by presenting self as hyper-sexual as a way to re-appropriate their own body. Of course - it's contextual. What one person chooses to present at one point and time can easily change as a reflection of the social construct. 

Here is an interesting article examining the question of gender and sexual trauma. 
Turchik, Hebenstreit, &amp; Judson (2015)

You might need an academic login

This one focuses on the differences between the two genders: Cashmore &amp; Shackel (2014)