Lindsay, for me this is the most important feminist issue. Caring about women's rights in the West is also important, but mostly to guard the rights that we have won and ensure that they aren't chipped away (in the form of general apathy, conservative politics, psuedofeminism, etc)...still, some of the things feminists talk about in the west are so trivial compared to laws confining a woman to the home, wearing a burqa, marrying preadolescents, honor killings, state-enforced punishment of rape victims, and more.
Some feminists have just said that they don't want to derail the conversation, be overbearing, etc...I'm sure women in danger for their lives really appreciate that cultural sensitivity. Meanwhile, other so-called feminists (Germaine Greer) have compared female genital mutilation to Western women wearing nail polish and high heels. Last time I checked, I was never forced against my will to do either and have still gotten to live a pretty full life without them. What this is is selfish. It's identifying with one's culture more than identifying with women worldwide. Cultural sensitivity is downright racist by having different standards for people based on their race or culture; "well, I would never put up with having my genitals mutilated, but it's good enough for people in the third world".
This "but we in the West should look at ourselves, we're not so perfect" is just cultural relativism in disguise, reluctance to speak badly about any other culture. When did we say we were perfect? Also, it's not like the Islamic world doesn't criticize the West for being godless, immoral, etc.