"Some people" are going to be rude and unpleasant about all sorts of things. You can't do anything about it.
Just remember that for every person who is rude, there are 100 people who dont' even notice, 100 who notice but don't care, and a couple hundred who think it's great that you're nursing your baby.
EDIT: To 'Give Peace a Chance" -- the problem with special nursing areas -- aside from promoting the idea that nursing is something that has to be hidden away, is that they just aren't convenient. If Mom is shopping at Macy's, and baby starts to fuss, is she supposed to leave all her stuff and haul a crying baby to the other end of the mall? Or finish her shopping while baby cries and THEN haul the crying baby to the other end of the mall? Sure, a quiet place where mom can relax for a bit and nurse is a fine thing to offer. But if should not be in any way complulsary.
And as for pumping and bringing a bottle along .. why? It's a lot of hassle, and if it's been a few hours since mom has nursed, she's going to be uncomfortable and leaky while she's giving baby the bottle she has so laboriously pumped.
The fact is that 99.9% of women who BF in public, whether they use a blanket, or wear normal clothes do so discreetly. If a person has issues with it, that person has issues with the fact that the baby is being breastfed ... NOT with any sort of indecent exposure. And a person who has issues with a baby being breastfed is a a person who has 'issues.'