I would allow the spell to work normally. My reasoning is that familiarity is an ambiguous concept. How does one develop familiarity? Is it by knowing facts about that person such as their name and trivia about their lives? If so, a person could be familiar and cast sending on individuals they've never even met. But if this is the standard, then that same caster might be unable to successfully cast sending to contact the barista they see everyday that gets them their coffee and engages in small talk.
On the other hand, does familiarity come about based on interactions and shared history? If so, the foremost scholar on Strahd von Zarovich could not use sending to contact Strahd since they have never met. But they could use sending to contact their neighborhood, who they don't know terribly well but still get together during communal holidays.
So it really depends on how you define familiarity. Is it about concrete knowledge of that individual, or the shared experiences and interactions you've had with them, or something in between?
Personally, I lean in favor of interactions over concrete knowledge. Magic is ephemeral and about energy. I see interactions and relationships as being able to create invisible links of energy or impressions between others, and I see magic being better able to follow such links more easily than concrete facts and descriptions which can be obfuscated by perception and context.