Have you ever run into your therapist or seen him/her out in public somewhere and what was your interaction like —if any?
I had a friend who ran into his therapist outside of the office and said he was really disappointed with how indifferent she was too him. She wasn't very friendly at all when he said hello to her. He was a bit upset. Later she explained that she doesn't engage with her clients outside of the office for
their own sake and privacy. He didn't really buy that. He felt slighted.
My friends who work in the field talk about how it can be awkward to run into their clients sometimes, if only for the fact that they need to respect the client's privacy and keep their own boundaries as well. My friend explained that a therapist usually won't initiate any interaction with a client because what if they don't want anyone else around to know they're even in therapy? (It would put the client in an awkward position if they're happened to be there with a friend, co-worker, family member, or possibly have mutual connections, etc.) So it makes sense that a T would never approach or acknowledge a client unless the client acknowledged them first. It also makes sense that the T wants to keep their own life separate from work. They have their own lives and can't be 'on' for other people 24 hours a day.
When I saw mine at a coffee shop one day, I wasn't going to bother her—for all the above reasons—and was a bit nervous about what would happen. I had the same internal response I used to have when I saw my school teachers out in public.

and thought back to my friend who had a bad experience. I didn't want to be disillusioned.
We ended up crossing paths anyway. She was very cool and asked how I was doing, and it was a nice but awkward exchange only because
I felt a bit awkward. I kinda froze and couldn't really chat about much. I wish I had it a bit more together to engage in better polite conversation but I'm horrible at small talk.
I also have a bit of a crush on her, so there's that. But I was sooooo secretly thrilled to catch a glimpse of her real life, 'off the clock' persona as it were, and happy she was hanging out in my neighborhood. I thought about it all week but of course when I got into session with her, it never came up. It was no big deal really.