I'm obviously unqualified to weigh in on the theological debates. But the column raises some difficult questions regarding the project of cultural solidarity. There seem to be two main tacks one can take. On the one hand, one can affirm the rights of the culture as it is commonly presented. The problem is that this, in effect, means reifying the power of the dominant actors within a given culture, at the expense of dissidents promoting alternative views (this was a point raised by Timothy Burke when talking about "cultural appropriation, see also Madhavi Sunder's superb article Cultural Dissent for more on this). This, of course, is what the authors are objecting to: by treating the hijab as the quintessential requirement of what Islam requires out of women, "solidaristic" women act to marginalize feminist dissidents within Islam that reject the hijab's mandatory place within the faith.
The other approach some take is to look for particular elements within a culture whose values seem to be consonant with one's own, and stand with those persons. Most western feminists in their own lives would, of course, fervently reject any demand that they wear a head scarf or otherwise obscure their bodies in a particular way. So they would express solidarity with Muslim women by expressing solidarity with those women who (like Nomani and Arafa) are struggling for similar liberation from oppressive gender norms within their own culture. The problem with this strategy is that it feels quite a bit like cherry-picking. Indeed, it's not clear how it's a form of solidarity at all: one isn't actually interested in cultural rights qua cultural rights, but is taking an external set of value preferences and hoping that the culture converts to adopt them.
There are no doubt some who read that last paragraph and thought "so what?" But one of the motivating instincts behind respecting cultures qua cultures, at least to some degree, is a justified suspicion that we lack a sufficiently thick socio-historical understanding of the relevant norms of the culture so as to be confident in our appraisals of what their particular practices really "mean". "Anything sounds bad out of context," after all, and context is often lacking when one is gazing at a distant culture from afar. Couple that with lingering attitudinal biases which can color one's appraisals of the relevant culture and there are good reasons to be appropriately cautious about one's instincts. That goes double when somebody from the culture comes up and starts saying exactly what you want to hear about it. These worries -- and they are legitimate ones; they're a large part of why I think some form of "respect for culture" is important -- are I think what prompts folks to swing sharply to the other side and adopt an uncritical solidaristic position (which I also think is ultimately harmful and untenable).
So there is a real difficulty here, and one has to be judicious between taking others as they are and a sort of blind "solidarity" which ends up being a rote ratification of pre-existing power. Culture is as it does, and I tend to reject claims that Islam "really" does or "really" doesn't require the hijab (and I view claims about what "is" authentically Jewish or American or what have you in the same way). These things are contestable and are borne out by practice. As a liberal, it is important to me that people have the right to engage in these contestations, so I think we should be appropriately skeptical of simply jumping in to affirm one side of the debate over the other. Ultimately, I think we need to respect the right of dissidents to dissent, but also need to engage with cultures as they are and not assume that they are simply being outrageous when there seems to be a divergence from our own view. Cherry-picking is what gets us "I'm not racist, Herman Cain agrees with me" or "I'm not anti-Semitic, some of my best friends are JVP", and that's not really a satisfactory response. The point is that actually respecting cultures while respecting cultural dissidents is difficult work, that requires considerable intellectual adroitness beyond that which is often admitted by the pure "solidarity" model.