AFAIK the term street epistemology comes from Peter Boghossian's book,
A Manual For Creating Atheists. It's worth a read if you want some tips for one-on-one dialogues with believers of various stripes, intended to promote critical thinking and doubt. The TLDR version: stay impeccably polite (though there are exceptions to this!); build a rapport; frame encounters as dialogues to get at the truth or the facts of the matter, not debates or intellectual gladiatorial combat; don't argue or put forward a case for atheism or any non-ism, and don't outright state that your interlocutor is wrong or failing at reasoning; but persistently and calmly ask pertinent questions that get at the heart of how the irrational belief in question is maintained. The above video is a great example of the techniques advocated in the book. I think they work best when you're face to face with someone, so you can pick up various non-verbal cues, and you can tell when to push or when to let a telling silence linger.
"Change will preserve us. It is the lifeblood of the Isles. It will move mountains! It will mount movements!" - Sheogorath