The phrase "perfect strangers" refers to people who do not know each other at all. They are complete strangers to one another, with no prior relationship or familiarity. Full definition
It's nice to be able to share your cat pictures with perfect strangers, but it's arguably more valuable to create a visual diary as an extension of your own memory. (discovermagazine.com)
-LSB-...] The modern economy works because hundreds of thousands of perfect strangers can trust one another. (faith.org.uk)
They may face questions from perfect strangers about being adopted, whether they invite the discussion or not. (adoptionlearningpartners.org)