As with Airbnb everywhere, whether a German listing welcomes pets is the individual host's decision, stated in the listing's House Rules section. Hosts with a standalone house or Ferienwohnung often welcome pets more readily than hosts in a shared Mietshaus (apartment building), where the building's own Hausordnung can rule pets out regardless of what the individual host would prefer.
If a listing is silent on pets, message the host directly before booking rather than assuming. German hosts can decline or cancel a booking if an undisclosed pet turns up, and Airbnb's standard cancellation terms rarely favour the guest in that situation.
Worth asking about specifically: any pet cleaning fee, whether there's a securely enclosed outdoor space, and how close the property sits to a park, forest trail or lake — useful context given the Bundesland-by-Bundesland leash rules covered in the Activities section.

