FWIW, I completely agree that Claridges were out of order & deserve the opprobrium being heaped upon them. But at the same time I don't think that viewpoint is incompatible with thinking that, if possible, a bit of discretion (as practised by the woman in the story) is common courtesy.
When I was feeding my DDs I knew that some people might be uncomfortable with it so was discreet (not to the extent of using a cloth, I have to say) when feeding in public/mixed company. Their uncomfortableness may have been misguided but what's the harm in taking account of other people's feelings? It cost me nothing and made life easier. Breasts have more than one function - they are practical and sexual - and to pretend otherwise is deluded.
Having said all that I do wonder about the veracity of all these breastfeeding discrimination stories.....I fed 2 babies for the best part of a year each in all kinds of public places and never once noticed so much as a raised eyebrow!