this might be a weird one but: how would quinn convince someone with an outside perspective that the institute and what they do is the best course for humanity ?
Not a weird question at all! I did dive into a bit of that aspect here, but the most straightforward answer is that she does this through action, not words. People value results, and Quinn recognizes that. A huge part of the fear of the Institute was that they were a completely unknown factor -- what little IS known is, well, not good, from their creation of synths to be used as infiltrators across the surface, to human abductions, and other morally grey areas.... Which is why the Brotherhood travels to the Commonwealth to stop them in the first place.
So, Quinn convinces the Directorate within the Institute that they need to step away from their isolationist tendencies (that worked only to further animosity and fear in the past -- ex: Brotherhood), and instead project an image of cooperation. As mentioned in the other post, they begin setting up security patrols to help curb dangerous wildlife, raiders, gunners, etc. to bring stabilization.
They share food supplies as well as the seeds/harvest from their research into purging radiation from crops. There’s obviously going to be the suspicion and questions, but over time, as people take more and more, as they become more and more RELIANT, the distrust of the past will slowly ebb. People will become dependent on it. Because of that, people will expect more (and in turn, become more complacent to) their benefactor, which will only help them further in changing the perspective and fulfilling their long-term goals.... Though that’s a dialogue for another time.
This isn’t woobifying their actions -- only dressing it up to be more palatable to the public. Every choice the Institute and Quinn make are lodged in reason. While Quinn is slowly shaping the structure, methods, and goals of the Institute towards a better path, she still isn’t entirely benign nor innocent due to her utilitarian methodology(considering what happened to the RR and Brotherhood), but she’s a far cry better than the Institute’s past recklessness and callous approach.