I have experience of renting in the US where you cannot refuse to rent to anyone, no matter what the landlord's individual prejudices are, and it is assumed that the parents are the best judge of what might or might not be safe or suitable accommodation for their children.
Landlords may refuse to rent to people who have pets. It is the only reason a landlord may state on an advert to refuse a tenant. Some take a declawed cat, some aren't fussy about claws, some stipulate no more than three cats total, some refuse dogs -- there are a lot of variations. The only way a landlord can turn away a family with children is if the size of the group is too large, according to local overcrowding ordinances, for the property to safely accommodate. There is usually an assumption that there will be a maximum of two people per bedroom.
And property has long been seen as an investment in the US too, but this has not stopped localities from making regulations that prevent racial or ethnic or other discrimination. Hispanic immigrants have challenged local ordinances on the basis that they discriminate against extended families (landlords may stipulate a nuclear family, afaik) or families with large children and therefore are directed against hispanics, but the fire codes have won in most places. A prospective tenant who gets turned away because of a credit check that turns up what the landlord deems an unreasonable risk may challenge this decision too.
Mostly, you pay a security deposit, and agree that this will be forfeit in full or in part and used for repairs or refinishing. While a rental property is always seen as an investment and income generator, it is assumed that any property will require some work after a tenant leaves; not paying the rent is another risk of being a landlord, and it is not a risk that is confined to renters who have children. A landlords' rights really should not extend to banning any group or class of people, imo. there are risks involved in renting to any tenant, not just those with children. It can be done and is done elsewhere and not that many landlords have been driven out of business. There's much more private than public rental in the US.