Rumour and gossip happen everywhere, all the time. It's deluded to think otherwise. And friendship groups aren't a series of 1:1 connections, I don't choose who my friend's friends are, nor do I choose my coworkers (who could absolutely make a personal judgement about me based on what they see). This is how socialization works. Anyone is welcome to opt out, but it's not a particularly smart way to try and make friends.

It's kind of funny that in a thread that's ostensibly about making new friends your advice has turned to how to choose which friends to discard.