Street epistemology, in its most general sense, is the application of epistemology outside of formal academic contexts. However, it most often refers to a specific set of techniques used to explore the belief structure of someone having a cherished belief. The goal is to help someone introspect on a belief by navigating such conversations in a way that is non-confrontational and can rapidly bring into focus the core causes of the cherished belief. A community has formed around the use of such techniques.
The conversation will often follow a similar pattern. Initially, a cherished belief will be identified, and the interviewee will specify their degree of confidence in it. Then, variants of the following two questions will be asked. First, the interviewee will be asked what is (one of) the main reason they believe what they believe. The goal here is to better understand the belief structure, so the question should be meant as inquisitive, and not as confrontational. Once the interviewee identifies a reason for their belief, they can then be asked how it would affect their belief if, hypothetically, that reason was proven, to their satisfaction, to be wrong after all.
If they say that it wouldn’t change their confidence in their belief, then it must mean there are other reasons that support their belief. It can often happen that they will give reasons they think will be persuading to their interlocutor, but that isn’t actually the foundation of their belief. By asking that question, one has therefore potentially avoided a long discussion on something that wasn’t actually a strong pillar to their belief.
That also creates a vibe that is more reflective / philosophical / inquisitive, rather than political / confrontational. It can be very difficult to think clearly when engaged in a political / confrontational discussion — it creates an environment prone to motivated reasoning, and can trigger a fight or flight response.