Question

Which part of this excerpt from Ralph Waldo Emerson's "Self-Reliance" conveys that it is ideal for people to respect others’ opinions but to care only about their own?
What I must do is all that concerns me, not what the people think. This rule, equally arduous in actual and in intellectual life, may serve for the whole distinction between greatness and meanness. It is the harder, because you will always find those who think they know what is your duty better than you know it. It is easy in the world to live after the world's opinion; it is easy in solitude to live after our own; but the great man is he who in the midst of the crowd keeps with perfect sweetness the independence of solitude.

Answer 1

"but the great man is he who in the midst of the crowd keeps with perfect sweetness the independence of solitude."

This is the line that conveys what you are asking. In other words, it talks about keeping your individuality even in a "crowd," or with others. But if you analyze it, he still does not encourage withdrawing from the crowd but being "in the midst" of society while maintaining your independence/ individuality.

Answer 2

"but the great man is he who in the midst of the crowd keeps with perfect sweetness the independence of solitude."