My DD is now 6 months old and pretty portable - rarely cries in restaurants/cafes now, will squeal or scream (for fun) sometimes because that's how she 'talks'. She loves going to these places because there's so much to see, smell, hear.
Up to 5 months old, however, she was pretty much non-portable. I couldn't go anywhere with her, not even the park. I mean, I would still go to the park because both of us needed the fresh air, but she'd be screaming all the way, people staring at us or coming up to me with 'advice' or to ask what was wrong with her, there was no way of calming her down, not even holding her would work. She was a difficult baby, and I don't doubt she's going to be difficult again in the future (but hoping not). But at least it happened during the summer months, so we could be outdoors.
I didn't sit in a cafe or anywhere else during that time. It was at times incredibly hard; it stopped me from socialising with other mothers who could take their children indoors. I was so worried about people staring and being uncomfortable, but to my own detriment.
Yes, it was my choice to have a child, but we were all screaming babies at some point, and our parents still deserved a decent life and a treat now and then.
A HCP told me once that those who don't like being around children in public spaces have the choice to stay at home, or go to places where children are not allowed. It's brutal, but the reality is that by going outside you run the risk of bumping into annoying people. Like babies, and young children. And people staring at their parents.
I do think crying children should not be ignored though, which is where the people in your examples went wrong. I'd pick up my child and try to comfort her, maybe go out for a minute, walk about the place while I tell her about what we're seeing, etc.