Governor Haley is a member of the Republican party which is the more conservative of the two main parties in the US. Furthermore, she is aligned with the right of that party and endorsed by the "popular" "Tea Party" movement, which by British standards at least would be considered to be quite right wing.
She supports measures to restrict access to abortion, including mandatory 24 hour waiting periods and the very controversial measure that women must submit to ultrasound (and if required transvaginally) and have the results explained to them before they can be considered for a termination. I believe she also opposes widening access to contraception.
I wouldn't actually expect a Governor with her "politics" to support measures to prevent or support victims of domestic abuse or sexual assault, either. Her philosophy would be that these aren't public health issues, but matters to be addressed by the extended family, the church and the community and if required, the criminal justice service or social services (i.e. removing children who are at risk.)
It might seem counterintuitive that a woman politician could support measures likely to have such a detrimental impact on other women, but there are plenty of examples of people who appear loyal to their politics way before they are loyal to their identity or other people like them.
Haley is also a woman of colour - her parents were immigrants from India and until her marriage to a Christian was Sikh. However, she has also supported very repressive policies on immigration, for stopping and searching people "suspected" of being illegal immigrants and has not supported measures that would encourage more positive "race relations." So, there's another seeming contradiction for you!
Not surprisingly, she's been subject to sexist and racist slurs by her opponents (both those who think she's too liberal and those who think she's too conservative,) which is unacceptable. Criticise her political stance, yes. Criticise her personal identity, no.
While her political views may seem hypocritical in the extreme, there is also a general philosophy within the American "value system," that any person can achieve whatever they want, that they can "rise above" restrictions like sex, race and class. I'm pretty sure she would say that that is what she's done (with the added statement that if she can do it, anyone can and shouldn't be pandered to.)