Solutions
Correct sentence is - While intellectuals can argue about the sources of Chinese conduct, peasants with their common sense can point to answers lying in plain sight
Both while and when are used when two things happen at the same time, but we tend to use while with two continuous actions and when with two single actions.
Right now, I’m recording a video while my husband is working. We have two continuous action, I’m recording and my husband is working. Both are taking place simultaneously and different actions.
when I get home, I take off my shoes. That’s also two single actions. I get home and I take off my shoes.One action ended, and just another action started. One action follows other.
I picked up the phone when it rang. First, the phone rang, and then immediately I picked up the phone. He came out when the bell rang.
According to the question
Action 1. intellectuals can argue about the sources
At the same time
Action 2. peasants with their common sense can point to answers