Why on earth should it not be okay to breastfeed in public? Do you go into private to eat? Would you banish a toddler having a sandwich to another room in case it offended anyone?
No, of course not, that would be ridiculous.
So is objecting to people breastfeeding in public. Breastfeeding is the best start to a childs life, its difficult to establish, with numerous stresses and possible problems; why on earth do you need to make it more difficult for people who are trying to get going with it? It is the "normal" way for a human child to be fed - formula is better than it used to be, but it is still a substitute and nothing compared to breastmilk.
I have been breastfeeding my son for eight and a half months now. And when he is hungry, he gets fed. I've fed on buses, in parks, in cafes, on benches, walking up the street... And I shall continue to do so, for as long as he wants to have breastmilk.
The question should more be "Why to people think they have the right to object to breastfeeding in public?". Breasts are for feeding. That's why we have them.