Hi Ryan,
Yes, I did end up contacting AirBnb.
They assured me that AirBnb does not link to my Facebook account unless I explicitly tell it to.
They guess that maybe Facebook has been tracking our IP address and somehow linking that to guests who have stayed here and also those who request to stay here.
Since we are trying to help protect our guest's privacy - who haven't given permission to Facebook or AirBnb to link up all our accounts - I have decided to delete my Facebook account.
You seem to be having a different issue. I believe that for many computer browsers, if you're logged into AirBnb, Facebook can figure that out, and vice versa. Maybe somebody else here can comment on that, though, or perhaps you can reach out to Facebook or AirBnb support to get help.
Regards,
Dan