The debate over Islam has been had too many times in other threads- but suffice it to say, any sort of essentialism of Islam as anti-feminist is incorrect ( There are Islamic girls who play sports, and there is nothing intrinsically anti-feminist about covering. )- or at the very least, antithetical to the opinions of Islamic women feminists. And hence the problem for those who want to indict Islam as intrinsically anti-feminist: it requires defeating the voice of Islamic women feminists who actually embody a feminist version of Islam. You have old white men like Richard Dawkins tweeting patronizingly against Malala Yousafzai, because "he's atheist, so he knows better durr". Anyone who thinks that's feminist has no clue.
I agree there are Muslim feminists, but they, like Christian feminists, almost always take their holy book less seriously and/or literally.
The more of a hard-line stance a Christian takes on "The Bible is the inerrant word of God and is absolute literal truth," the more anti-feminist he or she would tend to be.
To my understanding this is similar with Islam.
However, Islam, on average, has less wiggle-room than Christianity due to the lack of the Old Testament/New Testament dichotomy. So there are liberal Muslims, but they're rarer.
And requiring covering is inherently anti-feminist as no equivalent stricture exists for men.