Just found this, interesting!
This was a huge source of angst for me when I was breastfeeding. I understood that there were people who were disgusted with the idea of me breastfeeding my baby in their vicinity -- they were quite obvious about it. My choices, however, were a) stay home (I had just moved to a new city and knew nobody) b) be prepared to breastfeed at a moment's notice. From first signs to boob-in-mouth I'd usually have maybe 5 minutes if I wanted to avoid a complete screaming fit, which also tended not to go over well with the masses.
I overwhelmingly went to "child friendly" places with lots of other moms and babies, but there were still always people who were offended. When the baby was nursing, nothing showed, but Ms. Socialbaby had this patented move where mid-suckle she'd rear her head back and grin at whomever she could see, upside down, leaving me completely exposed.

I believe that other babies compliantly stay in place but she's never been one to pass up a chance to schmooze.
Can you guys imagine actually breastfeeding in a bathroom? How does that
work? There is one comfortable way to breastfeed -- sitting down, at a certain angle. If you're standing, your arms start killing you in no time flat. So you sit -- where, on a toilet? Does it have a cover? No, so do you just sit like you have to pee and then try to keep the baby from prodding you in sensitive places with a free foot? Do you sit down on the bare toilet with your pants on?
I did it, of course, but it was... yucky.
My local mall had a breastfeeding room -- I went to my local mall a lot, in those days. (Not that there was anything else to recommend it, except that it was not my house.) Peace be upon the providers of breastfeeding rooms. May they multiply.
I worked out a system similar to what Chai mentioned -- I started with a blanket but the baby would get way too hot and WAY too annoyed and it would be a huge struggle to keep it on her. I eventually settled on a thin cotton pareo with a high-contrast black and white print to hide what was going on under it. Easy to pack, too. Great.
She tolerated it if she was super-hungry, but would constantly be trying to get it out of the way and it was just this big stressful thing and it would make me so upset that this had to be such a big deal. Who CARES?
Thought of all of this when I was at the airport, was thinking of starting a thread on it. I was eating on an upper level with a central cut-out/ courtyard that had clear plastic guardrail things around it. A mom across the way was looking around and trying to figure out if the coast was clear for giving her baby some food. She (the mom) was clearly disconcerted that there was no particular protection offered by the guardrail/ fence. I wanted to send here some sort of "it's OK, don't worry about it" vibes, but my attempt at eye contact seemed to make her more anxious -- sozlet was off with E.G. and there was nothing indicating that I wasn't one of those "don't you DARE" people. So I averted my eyes, and thought again, who CARES?