I interpreted “they” in the second one as implying distance from the person in question, like the speaker wants nothing to do with them and is emphasising that they were a stranger. Possibly part of why saying “they” feels uncomfortable to people, but I’d never realised it until reading that example.
In my case if I don't know someone well, or at all, without thought I use gender-neutral terminology they/them/their and with pets and babies, again without thought, I naturally use it.
