I remember Paul's words, making it clear that he was not terribly concerned about how he was perceived by others, or even his own perception. That the Lord would be his true, and in a sense, only judge.
Others' view of us, to try to understand that, does have value, however. For example missionaries of the Christian gospel learned to live in a way that was better in sync with the culture in which they were living and witnessing. Like Paul they were learning to become all things to all people, to win as many as possible.
In Philip Yancey's wonderful book, What's So Amazing About Grace? I recall the story of a man who worked for civil rights for African Americans in the 1960's. But God put it on his heart to become a servant in sharing the gospel to people in the Ku Klux Klan. Without participating in the sin, he had to become identified with them. Perhaps in everyday ways. Ways that all humans share. Befriending them, in the reconciliation that God in Christ has provided for the world.
Others' view of us both doesn't matter, and it does matter, depending on what we mean. We need to contextualize the message and good news of the kingdom of God in Christ, as Paul did. That is, really seek to understand and know the people whom we are seeking to reach. Knowing that we are sinners along with them. In need of the same grace found in Christ, for us all.
What thoughts or experience would you like to add, here?