How I headcanon the Yotsu's would treat a cat on the street.
—Namikawa is really just.. superficial. That guy is superficial at many things he does. He doesn't care about animals, even finds them annoying sometimes, and would really just ignore any cat he saw on the street, maybe give it two head pats if he thought it might be good for his public image but the odds are low.
—The similar goes for Midou, though he might, reluctantly, get invested in it if it lingered near him long enough and Maybe take it in if someone put the idea in his head (I'm just thinking about Midou/Shimura) He probably calls the cat insults while being affectionate too.
—Shimura is a cat person. I can't prove it but I just KNOW he owns a cat. He is very careful, so sadly, he wouldn't be petting any cat outside unless he was planning to take it in. He is just worried his own cat might get a disease :(
—Ooi is more of a dog person, I headcanon that he owns a dog too. But he likes cats as well. He might even let it sit on his lap for a few minutes.
—I really don't know what to say for Kida. He isn't a character I think about a lot. I headcanon that he is kind of a clean freak so he wouldn't like street cats.
—Takahashi is definitely affectionate with cats. He would also try to make a good example for his kids by being kind towards animals, I think.
—Hatori is very similar to Takahashi but just more affectionate. He might even have a cat of his own.
—Higuchi is a very shallow person and unlike Namikawa, he isn't smart enough to understand that how he acts might affect his public image. He might kick the cat if it annoys him too much.