This doesn't really count since it's only online I've come across it but I was really shocked and quite upset by the routine nature of infant circumcision in America when I first found out about it. I just couldn't understand why people were so blasé about the idea of something being cut off their newborn. If it was any other surgery, people would be filled with anxiety and worry but this is as normal to many people as vaccination, and I can't get my head around it. It also baffles me that insurance providers cover it and modern doctors recommend it when there's so little evidence that it has any benefits. You can also add declawing cats and removing the voiceboxes of dogs who are considered nuisance barkers to this alarming list.
From living in Germany, a few things. Yes to whole kindergartens full of children being taken off on trips just randomly with no mention to parents and none of the safeguarding/risk assessment you'd get in the UK. They are also really relaxed about small children being around open fires to a weird extent. I also a couple of times went to pick up DS and his friend would follow me and the staff would cheerfully say "Oh are you going with X today?" 
Actually, that did stop when management changed but it was slightly alarming! Now DS is at primary school, and his school site is in the town centre and is completely open with a fence only on two sides, and only really to establish the boundary. Anybody can walk in and any child could wander out. Whenever I go in to pick him up even outside of normal start/finish times I never get questioned about who I am or what I want unless I look lost.
Children in public often seem to have their volume control set to a significantly higher level than British children. I think this is partially because they are often allowed out on their own from about 7 and from about 8 or 9 they travel in groups with no adults present commonly, but even when you see really little children with their parents or grandchildren the children speak in ear splitting tones (as they do) but they don't get told to shh or keep their voice down because the whole carriage doesn't want to hear their conversation Schools and kindergartens here also tend to use public transport instead of hiring their own minibus or coach, so you sometimes get on during the day and a carriage and a half is full of bickering/excitedly shouting children 
oh and they have the most ENORMOUS school bags which have a tendency to bash into everything when they turn around (and you have to buy the stupid bags which cost hundreds of euros too).
Getting work as an English teacher on the basis of being a native speaker and just being expected to randomly teach groups of children unsupervised with no police background check and no training to teach children or safeguarding training. These groups are often held at crap times so the children are tired, bored of school, hungry and hence awfully behaved but there is often no higher authority to report behaviour to or behaviour management system in place. (I think this is far more to do with a culture of poor practices in the TEFL industry than any particular country, to be fair, but still.)
Also not being able to buy simple painkillers or other off the shelf remedies (e.g. for cystitis, worms, thrush) in ordinary shops and a general perception that such a practice would be horribly dangerous to health.