Can landlords exclude tenants with children?

I wonder why that is? It's not allowed in most places in the US, because of fair housing laws.

My apartment complex has that rule for the building that houses the rental office. I would have been in that building except I have a cat. Sometimes when the neighbor's children are loud I wish I hadn't told them about Chloe! 

I can understand the landlords wanting to refuse children and pets, but it does make it more difficult when you have pets or children to find a place.

For the plans to have children, I think that if someone is renting a place on the condition of having no children or pets that it's a fair question, it's meant to be in keeping with the agreement and I don't see that as discrimination. I wouldn't be offended.

FWIW, our flat in London was "no children" but our landlord never asked us when we rented it, and we told him when I was pregnant and he was fine with us staying on as long as we wanted, but we did tell him we wouldn't be there long term.