[pluma]

In Germany cats are considered small pets and it is illegal for a landlord to prohibit keeping small pets in an apartment (within reason -- there is case law to help out with edge cases). It's often found in contracts but the clause is unenforceable and legally void. Dog owners always have to get explicit permission. In either case the right is null and void if the pets grossly misbehave (damage to the apartment or unacceptable noise levels that disturb the neighbours).

Due diligence aside, documented evidence only comes into play if you become aware of it. If your tenant is posting pics of a pet they're not allowed to keep in the apartment but you're not aware of the pics, no problem. If you pre-emptively ask for their social media details and then neglect to act on the information you find, sure, all blame on you.

There's an important difference between being made aware of information and actively seeking it out. Morally there's no difference between a landlord denying you an apartment because they've been shown a tweet of you bragging about doing property damage or because they were actually there and saw you do it. But there's a world of difference between either of those and intentionally rummaging through a candidate's social media presence to actively look for grounds of denial.