It may be hard for us to fathom, but tradition tells us that St. Paul was not a very good public speaker. I suspect that we have come to believe that because he wrote skillfully that he must also have been a skillful preacher. Supposedly that was not the case.
So when St. Paul tells the Church of Corinth that he is not concerned about how others judge him, he is probably addressing another source of contention in the community; namely, those who counted themselves better than others because they had been baptized by Apollos who was reputedly a remarkable orator.
Later on in this very same letter, St. Paul will write a very recognizable passage on the gifts of the Holy Spirit and the fact that each Christian is blessed by gifts to be used for the good of the community. I am sure that you remember the passage in which he speaks of those who have the gift of tongues, those who have the gift of the interpretation of tongues, those who are gifted teachers and administrators, etc. The basis for that passage might be said to be set up by the passage that we read today. St. Paul recognized that Apollos was better than he was in the public speaking department. He writes that that should not make any difference. Rather, he says that we should regard everyone as a servant or steward of God.
A steward was someone who was charged with the care of the master's estate, the master's wealth. St. Paul, indeed every follower of Jesus, has been charged with this task. We are to care for the gifts with which the community has been blessed, gifts that are manifested in its members, gifts which have been given for the express purpose of building God's reign. If we act as good stewards, then the judgment of society counts for naught. God's judgment is all that matters.