I have synced my airbnb bookings to a google calendar I made up for that purpose, and I then shared the google calendar with the person who helps me care for my property, as well as sharing it with myself, so that it also appears on my main google calendar.
One thing to note was that when I synced from airbnb to my google calendar, it did not appear as an editable event, and would NOT transfer to other shared calendars as a result. Each time I've had an airbnb booking transfer to my google calendar, I have had to manually duplicate the event, (right click on the event, and duplicate onto calendar is an option), which made it then appear as an event on my google calendar, and then it transfers to the other shared calendars. I then deleted the original posting that synced from airbnb, otherwise I would have duplicated listings.
A bit cumbersome, but it has solved a similar problem for me.