There was a famous story back in 1997 about a Danish mother that left her toddler outside the restaurant. Some practices for behavior in public, common and accepted outside the US, might be illegal or considered "shocking" in the US. This could be surprising to new immigrants. I am not referring to anything as barbaric as Female Genital Mutilation, but things like leaving your child home alone when he/she is in grade school and the like.
Are there other "benign" practices, that are acceptable in much of the world, that might be considered illegal or out of the norm in the US? Or are there any guides that one might refer to for this kind of information?
Well, it would actually be good to build a country-by-country list.
Let me try to enumerate the high level hot points and I will allow others to help fill these out.
Privacy in public. Unlike many many other countries, if a stranger disagrees with what you are doing or has an observation, it is not uncommon for them to speak to you about it. For instance, to be told in the supermarket, by another shopper, that you are being too cruel to your child or that you are not controlling them enough. They may try engage in a dialog, or they may just shout their observation and then walk away. You are not bound to follow the instructions of the stranger; just be prepared for this to happen. Parents are broadly understood to be responsible for their children's behavior, e.g. tantrums in public places. This principle also applies to all of the following points:
Childcare. You should expect a young child to be accompanied by an adult or in a physically secure location at all times. People have occasionally fallen foul of the Law by letting their children walk to/from school. Americans are afraid of "kidnappers", strangers who would pull a child into a car and take them away. (This is extremely rare and most children "kidnapped" are simply taken by their own parent, against the instructions of a court order.)
Sex. Americans are concerned about any sexual activity or language near children. This extends also to non-sexual nudity of adults. So, if you walk around your home naked in view of your children, this would be viewed as "strange". If you live this way, best simply not to tell anybody.
Breastfeeding. Deserves a topic of its own. Plan to cover up when breastfeeding, until you discover otherwise that it is accepted. This varies widely, and many Americans have surprisingly strong opinions either way.
Child nudity. Similarly, Americans also expect a child to be clothed when in public. For example, if a 4 or 5 year old child were playing naked, in your own private back yard, this would be observed as "strange".
Diapers. Likewise, avoid changing diapers in public view. In New York State, male members of daycare staff are prohibited from changing babies!
Private transportation. It is critically important to always have a legal and appropriate car-seat for small children when they travel in a car. People are very serious about this topic, and as a point of honor will to instruct you themselves, or will call the police.
Public transportation. Do not expect strangers to offer to help you with a pram. Widely, people are expected to be able to navigate and carry whatever they travel with. If you ask an able bodied stranger however, they will help. If you have a foldable "stroller" you will often be expected to fold it up and hold the baby to save space. Prams are definitely not in the same protected category as wheelchair users. You should never expect special treatment.
Strangers. Older children who can talk are fairly universally taught "not to talk to strangers." This is to avoid them being manipulated by molesters. You can expect your own children will be taught this principle as well. If you do make a friendly remark to a stranger's child while shopping for example, you can expect to be followed around by the store's security staff. American children are welcome to approach uniformed police offers and will be treated kindly. More practical advice is for them to approach a "grandmother with children" when they feel threatened by a situation. Nevertheless, the prevailing attitude is that child rapists are anywhere and everywhere; parents and children are instructed to maintain a vigilance against the perceived threat.
Violence at school. Monitor your school aged child in case they may be expressing bullying behavior or be the victim of bullying by other children. Go to your child's teacher for advice in this case. American boys are broadly encouraged to learn basic fighting skills so they can defend themselves; the respected American behavior is to fight back when attacked.