It seems obvious to me that focusing on doing the right thing is good, while focusing more on managing everyone else’s impression of you is bad. In fact I thought everyone knew this.
A lot of really bad people didn’t care at all what anyone else thought of them.
Status, like it or not, is a huge determining factor in opportunities. You can do the right thing all you want but if people think nothing of you, you might not get very far.
This is coming from someone who doggedly believes in doing the right thing and lost status many times for doing what I thought was right. It doesn’t always work out.
Managing everyone's impression of you is how I understand you're supposed to make friends. If you don't fit in with a group then they'll stop wanting to be around you and you'll no longer have them to talk to. Arguably having a single friend is similar to the idea of being part of an exclusive club without the pointless vanity; on the contrary it's a critically important factor for not going insane from isolation. The tradeoff for receiving that benefit is you have to acknowledge their wants and needs instead of always acting in your own interest, and coexist with them peacefully.
If you're generally doing good things, you don't need to spend anywhere near as much time managing your public reputation. Obviously you can choose to, but it'd be by choice and not out of desperate attempts to glorify meagre deeds or cover-up bad ones.