Keeping to your theme of animals:
Red flag:
If they identify as either dog or cat people. Dog people anxious attachment i think and cat people are avoidants! Thats my theory which I will now get destroyed 😅 just purely from personal experience
If they dont like people, say they like animals more than people, just vocal about animals over humans: even though i get it i find they tend to be too complex, traumatised and fragile for any closeness, very touchy and volatile.
If they think there are no dangerous dogs just irresponsible owners or if they leave big dogs unsuperviser around babies they are a red flag to me for being thick and irresponsible
If they keep pet rats or snakes, weirdos.
Green flags:
Brings proper suitable feed for wildlife not bread
Their pets are a healthy weight
They look after the dental health of their pets
They don't declaw
They don't hoard animals or keep animals they have no space for eg super active dog breed or cat in a small cluttered home in the city
They adopted their animals instead of purchased.