I find this quite a difficult question. Obviously the easy answer is "I don't give a damn".
However ... when I was a working man I had a job in which, in important ways, my public reputation in my profession was relevant to my career. For example, in order to gain promotion I had to show that only did I have esteem from my peers on a national level but also that I had an international reputation - as affirmed by my panel of international referees. It is probably fortunate that this did not really dawn upon me until close to the end of my career. I had spent my time doing and saying more-or-less what I liked and it was only later that I recognized that other people liked it too.
I also published quite a lot of stuff. Now one thing an author needs is readers; if nobody reads what you written then you haven't really "published" it. It is just some dusty old thing sitting on a shelf somewhere. So I did care what readers thought.
I was also for many years a (voluntary, unpaid) trade union representative. I was supposed to speak for other people - for my union branch at regional level and for my region at national level - and so obliged (so I thought) to report back to them so they could decide whether they liked it or would want to elect somebody else to represent them.
In these ways other people's opinions were important to me. I suppose I would say they were definitely my business. But I wouldn't necessarily change anything I did, or am doing. because of the opinion of others.
