I kinda live in a small city, so I can relate to what you‘re to talking about.
With my first T, I would occasionally see her if I went to a sport event, but this was a rare occurrence. Also, I had a mutual friend with her son in university. But, it was never a problem because we had discussed this, and agreed to not call to each other if we saw each other in public. I preferred it that way because I never wanted to have to explain to anyone who she was. I don’t see her anymore now.
My current T though is someone I see at the university I attend, so I see her more often outside of therapy, sometimes 2 or 3 times a day (because of COVID-19 this doesn’t happen anymore). This was quite worrying at first, for a couple reasons. I don’t talk about being in therapy with my friends, so I was worried they would find out. I was also worried that she might approach me when she saw me, especially when I was with other people, which could potentially lead to me having to explain why I know her. Plus, I had a couple professors that worked in the same building that she worked in, so I was worried about what they might think when they see me going to her office every week for my appointment. And, I just found it quite awkward and uncomfortable having to see her every day, knowing that she was aware of my past trauma.
All this took a lot of getting used to, but we made sure to discuss how to handle seeing each other outside of sessions, and agreed to not acknowledge each other. With professors that I would see, we might call to each other but it has yet to become a problem for me (I probably was just overthinking about how they would perceive me). With friends, I have been able to admit to them that I see a therapist (although not the reason for it), so the fear I did have about having to explain anything to them isn’t there anymore. But, something positive that I never foresaw was this actually being somewhat helpful to therapy. My therapist said that being able to see how I interact with people outside of therapy has allowed her to understand and better address the concerns around interconnectedness and how I relate with others, and I can better explain things to her based on what she’s seen. It’s been almost 2 years since I’ve been seeing this therapist at my university, and although I was worried about all this at first, so far it hasn’t been a problem for me.