It's not extenuating circumstances, @Kathleen8 . https://www.airbnb.com/help/article/1320/what-if-i-need-to-cancel-because-of-an-emergency-or-unavoid...
You also cannot discriminate against families by denying them when traveling with an infant. You can tell the guest all the reasons that having a baby on site is a horrible idea, but they get to assume the liability should they choose to stay. https://www.airbnb.com/help/article/1405/airbnb-s-nondiscrimination-policy--our-commitment-to-inclus...
Now, you have some options:
First, require that all people are counted in the headcount of guests. We require this and that means a couple traveling with their toddler cannot stay with us because our max guest amount is 2. Babies under 2years old are somehow seen by Airbnb and not needing to be counted nor do they charge for them. It's BS - someone renting a single room with their newborn triplets - ridiculous! So you have to be more crafty if this happens.
Second, when someone books with an infant/baby, tell them in unflattering terms, why staying with you is a bad idea. We tell them about:
- the lead paint,
- the open fireplaces,
- the insulation in those fireplaces that is easily accessible, sometimes bits fall out - please look at the pictures of the 115-year-old brick, the concrete hearth, and we have 3 of them, one in your room,
- our dog,
- the fact that NONE of the furniture is attached to the walls creating a fall-hazard,
- that our hardwoods are historic and sometimes splinter which would be bad for baby's feet, knees, or hands,
- we've never had children so we do not know how to create a place where children live, so our house is set up for adults only with expensive furnishings and antiques - which they would be financially responsible if damaged,
- that we have ZERO baby-proofing and alcohol, outlets, dangerous knives, and cleaners are within reach of little hands,
- the floors are uneven so a toddler could easily trip and fall into any number of sharp corners
- that since we would be worried about them and the security of their child, we would feel compelled to be on hand resolving issues 24/7 and we don't think they would be able to relax with our hovering around,
- plans we might have for that night which will require us to come in after 10pm and their room is right by the front door, which might wake the baby,
- AND if they haven't cancelled yet, we remind them that we have STRICT quiet hours between midnight and 7am so a crying baby cannot be in the house or it would be a violation of house rules that may require them to leave immediately.
You make it uncomfortable to bring a child, tell them all the ugly reasons why, and don't sugar-coat that it's not a good fit. You cannot choose for them, unfortunately, but it's no skin off your back to make your property sound crappy and dangerous so they self-select to cancel.