For personal growth, or turning you away from going down a bad road, you absolutely should care about what those you care about have to say about you, and very little about what random people on the internet who care nothing for you think about you.

For the sake of being a representative of Christ to the world, you should care what all people think of you. Ensure that they hate you for the sake of the gospel itself, not the way you present it.

"Let your speech always be gracious, seasoned with salt, so that you may know how you ought to answer each person." - Colossians 4:6 

"Keep your conduct among the Gentiles honorable, so that when they speak against you as evildoers, they may see your good deeds and glorify God on the day of visitation." - 1 Peter 2:12

"Show yourself in all respects to be a model of good works, and in your teaching show integrity, dignity, and sound speech that cannot be condemned, so that an opponent may be put to shame, having nothing evil to say about us." - Titus 2:7 & 8

"Moreover, he must be well thought of by outsiders, so that he may not fall into disgrace, into a snare of the devil." - 1 Timothy 3:7 

If our Lord tells us we should care what others think of us, not for our own sake, but for the sake of the gospel of Jesus Christ, then we should probably listen. 

 Amen, no need to fear man, but fearing God puts you in a position of caring what your fellow man thinks