Comparing breast feeding to sex is quite telling of how our culture sees breasts, whether we want to admit it or not. The more accurate analogy would be to imagine the OP's friend hiding under a blanket while she eats sandwiches because she didn't want her kids to see her eating sandwiches.
Which makes me wonder... if the friend was acting this way, while we'd obviously all find it very strange and shake our heads over this woman's issues, would she be getting the same kind of censure? Especially if we knew that the reason was that she came from a culture who had similar (if less extreme) views about the desirability of eating in public? Wouldn't we see her as something of a victim herself, rather than insulting her for her role in perpetuating the problem? I suspect that if it wasn't an issue as hot-button as nursing, we'd be seeing the inappropriateness of this sort of 'how DARE she behave in such an outrageous way' attitude more clearly.
And one other thought - it does seem to me that this level of outrage over breastfeeding/sex analogies is at least partly indicative of how our culture sees sex. Why else is it such a problem to draw an analogy between breastfeeding and another activity that's wonderful, pleasurable, hugely important to most of us both individually and in terms of survival of our species, and frequently a key part of relationships with our loved ones? Why should that be a poor comparison with breastfeeding?
Of course, some of it is because it is pretty much universally accepted that sex should remain part of the private realm, and many people do use the analogy as a way of claiming that breastfeeding should be subject to the same level of sanction in terms of privacy. But I hope I've made it very clear that I was absolutely not trying to do that with this analogy; rather, I was using it as an example of how individuals (rather than public custom) may legitimately choose to keep an important and positive part of their lives private, without it reflecting negatively on them as a whole. So why is there so much objection to this analogy? I do think that at least some of it is because of the widespread belief that there's something wrong or 'dirty' about sex, and so comparisons with breastfeeding are often assumed to be a way of saying something negative about breastfeeding. Which is a pretty sad comment on how our culture sees sex.