Disclaimer : Here are just some ideas. This outline is not meant to be taken as the only or final answer to the question.
1) Some may argue that it should not matter because everyone should have the freedom to do what they want in private. It is their inalienable right.
2) To add on, whatever they do in private should have no effect on how their work is judged. This would help maintain fairness and meritocracy. (Credit to Elaine 🙂 )
However sound the above arguments may be, these do not seem to be categorically applicable.
3) People in the public eye have a responsibility to be good role models because they influence so many people. Since their private lives are put under scrutiny, what they do in private does matter. (Credit to Najiy 🙂 )
4) In certain areas of work, what a person does in private affects the integrity of his work and can tarnish the good work that he does. So what he does in private does matter.
5) When the private action is criminal and wrong, then that person has to be taken to task for it regardless of the quality of his work. It can even be argued that his good work cannot be used as a mitigating factor in deciding the consequences of his wrong-doing if he has caused harm. (Credit to Irfan 🙂 )
6) On top of this, what a person does in private matters because the good quality of a person’s work could belie a harmful, unhealthy condition. Of course, this could be true for only a minority of people but the message here is that there has to be care for what goes on in a person’s private life even though he appears successful in his work. (Thank you to Dhanya 🙂 )
7) The arguments above point to a common idea that a person’s public and private life can be hard to distinguish. This is reinforced in this day and age when so many people make their private actions public using social media applications. Everyone who uses social media must be careful lest their private actions have an impact on how they and they work are judged.
8) Finally, private actions matter because after being caught up with the sudden freedom to over-share their private lives online, people in modern societies now have to rise above their heightened vulnerability in the internet age. Their caution over their private actions cannot be based on a fear of being exposed. That would be hypocritical. A person ought to set standards that he can live by through and through, not just when it serves his work. Even if a person does his job well, his private actions matter because the public and private domains of a person’s life are actually not that divisible after all. (Thank you to Olivia for this powerful idea 🙂 )