In order to make calendar and booking unavailable can use the option that allows to Owner to add iCal feeds to listings and add an iCal from a platform (like Airbnb) that has the option to block all dates in the calendar and mark it as booked.

Help for Ical feed feature: iCalendar Import / Export

Example of how to block dates on Airbnb and export iCal from their platform with all dates booked.