Breastfeeding is legal. And for a hairdresser to stop cutting and ask someone else to finish the cut well that is rude and humiliating for the mother. It is not an 'acceptable' compromise. The mother has every right to kick up a stink.
I find the argument that the mother needs to be considerate of the hairdressers uncomfortableness to be ridiculous. If people pandered to everyone that was uncomfortable with breastfeeding, serving black people in restaurants, working women ..... Then we'd still be living in a world where women stayed home all day, had slaves to help with the housework... Well Im sure you get the picture I'm trying to paint.