I'm probably the weird one here.
I breastfeed. In public. All the time. If I'm out and about, I breastfeed covered IF I CAN. Sometimes my daughter is adamantly hungry and will not allow herself to be covered. I can't always make it to a private location and I refuse to BF her in a bathroom (GROSS!). 9 times out of 10 though, she is covered.
I wear clothing when going out that allows me to breastfeed easier. I wear a tank top type shirt and then a shirt over top. I pull the top shirt up, leave the bottom shirt to cover my belly, and then just the nipple has to show. Keevia covers that quite nicely. I try to cover her head because she has a tendency to pull off without notice.
I do not cover up in my car usually. Usually she's STARVING by this time (I babywear and by the time we get to the car, she's been asleep for a while and wants food and wants it NOW), and its generally just easier not to cover. I'm in my private car, I have tinted windows, if people look, thats their problem.
My child's right to eat trumps everything else. I have pulled my breast out in the middle of wal-mart before because she was screaming bloody murder. Granted I was in the baby section, in a corner, with my back to the store, but had anyone saw me, I would not have been ashamed. I'm pretty darn modest when it comes to anything else, but my child has a right to eat.
So, I try to cover, and normally do. I don't have a problem with the women who don't cover -- that's what God made breasts to do, and I believe that breastfeeding is a beautiful thing. I don't judge them, because having a baby who is a hard latch sometimes, I realize that you will do just about anything to get your baby to eat. I chose to cover myself because of my religion mostly, but I can't believe that my God would want my baby to starve either.