Personally I find breastfeeding disgusting and prefer not to see it. This is 100% my opinion and I expect nobody to cater towards it. It's also the second most intimate moments a mother will have with her child, second only to child birth. For this reason I will always prefer my wife to do it behind closed doors. I don't want to share the "wonders of raising a child" and all that with people I don't know. This is family stuff, to be kept in the family (in my case).
That said, it's not my place to judge others for their family habits, some might relish in the idea of sharing their moments with the rest of the world and I respect that and keep my opinions to myself.
Where do you draw the line though? I mean, was this lady sitting inconspicuously in a corner doing her thing or was she parading down the middle of the museum twirling in circles and intentionally showing off with a nipper sucking on her nipples? And whilst she should be allowed to breast feed, if the museum provided a suitable room or area to do so privately, should she have respected their will to have her do it in there?
As always with this topic, there are too many variables to come to a solution which keeps all happy. We have age differences, cultural differences, family values differences, etc. What annoys me with this kind of thing however is the need to cater to a minority as if they're some gift from God. No love, you're just another woman with another pair of norks with a toddler hanging off them. If other women can get through life without having to make a stink about something as silly as this, why can't you?
The term "*********" comes to mind.