What zeeba said. We're all primarily responsible to ourselves and our babies when we're nursing, not to everyone else who has an opinion on it.
There's no right or wrong way of doing it - it's personal preference.
The transition to motherhood is a huge change, and people have to adjust to all sorts of differences. To a great extent, the mother's needs become entirely secondary to the baby's needs. No-one has any right to judge any other woman for the way she makes the transition from a completely autonomous and independent person, into a nursing mother with a dependent baby.
Even if we lived in a society which venerated nursing mothers, where they were given a standing ovation every time they fed their child, it would still take most women a little time to adjust to revealing a part of their body that is normally hidden. Most people don't have the ability to switch mindsets instantly. Before you have a baby, you don't habitually show your breasts in public. After you have a baby, it is suddenly permitted. You don't instantly stop being aware of the fact that this is a part of your body that is normally hidden. Women shouldn't be judged for how they manage that change.
And there is an element of judgement/criticism on this thread. People say that it's not the mother's fault that she is being made to feel this way, and in the next breath they say that breastfeeding won't ever be normalised if people don't see it happening. That makes it the responsibility of nursing mothers to make breastfeeding visible. But what if they don't want to?
Plenty of women do. The ones who don't should be supported and encouraged to do whatever makes them, and their baby, comfortable. I would hate to think of a nervous new mother reading this thread and feeling that she's being judged by one group of people for feeding at all, and another group for the manner in which she's choosing to feed.
Instead of feeling sad for women who are choosing to do things in a particular way, wouldn't it be better to look for ways to help them make that adjustment? If a woman looks like she's nervous and is desperately trying to keep herself covered in a café, why not offer to swap seats with her if yours is in a quieter corner? Ask her if you can get her anything as you can see she's got her hands full with the baby? Both of these things were done for me when I was feeding DS2 and it doesn't half help you relax.