1. I firstly always consider those who are living. If it's going to be deeply distressing or humiliating for a living relative, negative about them or adversely affect them, then there's no question I'd keep it on the down-low.
2. I also consider whether social attitudes have changed on the issue at hand. For example, illegitimacy has no social stigma now, so it doesn't trouble me to find out about that or share it. Nobody who hears it is going to think any the worse of my ancestor/relative now. In fact, often it's quite the opposite: people have more admiration for them for having faced adversity, or they enjoy having a connection to a good scandal or a total scoundrel.
3. If I think it will be a bit upsetting to someone, I may still share if I think there's a greater interest or another angle on things. For example, there are some cousins who might find the lack of genuine Scottish DNA on the part of Samuel McPherson a cause for concern. However, I maintain ongoing interest in all things Scottish is perfectly appropriate to those descended from someone raised by a Scotsman. It was part of how Samuel was brought up and what he was taught. The fact his actual genes came from elsewhere doesn't alter or lessen the impact that has had on our family and their identity. We know he saw John McPherson as his father. Not only that, I think the story of his true biological heritage brings another degree of richness to our family, and has always been part of our family story too (you can't turf his 'real' dad without turfing his 'real' grandma, who it turned out was also part of the heritage we'd been handed on.)
Apart from that, I've got to say I'm from the Publish and be damned club. Nobody wants to read a genealogy which makes the entire family sound like a bunch of sanctimonious fuckers. In addition, I'm not a big fan of cherry-picking in any form of life: you deal with the facts as they are and in their entirety. Then of course there's the fact that I'm generally lacking in gentle/subtle approaches or the ability to give a shit what anyone else thinks: those who know me personally know that for me, every day is Tell It Like It Is Tuesday! (I am, conversely, very hard to offend or upset.)
In answer to the title question, is there a 'right' to do genealogy? I say 'damn straight'!