I first came across this woman when I read her memoir Infidel in 2008. Since she was hailed as a radical atheist and endorsed by Richard Dawkins and Co I expected her writing to be full of half-baked, anti-religious polemic (one reason why I just can't respect Dawkins, to me he is just an arrogant, angry old man) but instead found her writing to be engaging, insightful and despite her strong opinons it was obvious that she tried to be fair and base her opinions on facts.
Her is an article about her and some excerpts from her new book Nomad:
Ayaan Hirsi Ali: 'Why are Muslims so hypersensitive?' | World news | The Guardian
Ayaan Hirsi Ali: Extracts from Nomad, her new book | World news | The Guardian
Personality-wise I would say she is an INFJ or INTJ leaning more towards the latter. She is soft-spoken, intense and seems to be on a mission. She is definitely very independent-minded and a thinker but as I said what struck me about her writing was that she tried to see all sides of an issue and to be fair instead of just mowing everyone down with arrogance who doesn't agree with her. I can completely relate to her characteristic of speaking the truth even if it is unpopular but trying to do so in a civilised manner, that's what makes me think INFJ. However I am not sure if an INFJ would be THAT provocative in some of their statements so maybe she is an INTJ after all.
I definitely got a soulmate-vibe after reading her memoir and have loads of respect for her despite us being on opposite journeys in life (I was brought up as an atheist and became a born-again Christian as a young adult while she rejected her Muslim faith and is now promoting secularism.) so that makes me think that maybe we are both fellow Ni-users.