@Jackson186 , I know that the times we have traveled/stayed to/in Mexico, copies of our passports have always been requested (at time of check in-typically hotels/resorts).
Granted, we haven’t stayed in an Airbnb property in Mexico as of yet but we have an upcoming trip next month, and will be staying at an Airbnb in Mexico City. Host(s) have not, as of yet, requested copies of our passport's. But I do understand that there were changes to Mexico City Tourism Law in April of this year. Not sure if that change required all host(s), both private and hotels, to require copies of passport's.
Best—