I guess as a parent of a potty training toddler, at home having the potty out and around the house is pretty normal... when first starting out there was a potty in every room! We actively tried to make going to the potty a fun and normal thing for him to do. So I can understand the parents being a blasé about it.
I also have a fold up portable potty with liners that lives in the bottom of the buggy for emergencies. We live a 15 (30minute at toddler pace) walk home from town and despite taking him to loo before setting off it's sods law we will be half way and he'll decide he needs a wee. So a couple of times he has used it in the park. He's also used it on the beach and on days out to outdoors places that it's a big trek to the nearest toilets.
BUT that's in our own home and outdoors! I would never get the potty out somewhere where there's a toilet within reach (the folding potty also can fold out to be a toilet seat). I also wouldn't get the potty out right in front of strangers. I don't want them seeing DS pulling his pants down for a start. Other parents of toddlers may be used it, but other people aren't.
I wouldn't dream of getting him to go for a poo anywhere in front of other people. They really don't want to see that! Luckily DS has regular habits so we started out with the rule that poos don't go in the potty they goo in the loo .... cleaning out a pooey potty is horrible.
As for the hygiene aspect though - I don't think a toddler having a wee in a potty is actually that bad (poo is different issue) ... maybe I'm just not a hygiene freak, but I don't see what the issue is? Yes it could get kicked over... Yes they parent and child should wash (or at least anti bac wet wipe) their hands. But as long as emptied straight away and cleaned hands it's not really a biggy.
But there are plenty of other skanky things I see loads of people do that bother me more: not washing hands after going to the loo, picking nose, letting babies crawl around on pub floor, wearing outdoor shoes in swimming pool changing rooms, wearing outdoor shoes all round the house..... But that's another thread!