I have read stories of very early missionaries who took on the culture of the people they were ministering too. China and Japan were two obvious ones because of the extreme nature of dress and hairdo that went with the cultural experience.
With my desire to move to a Muslim country, I try to see what I might look like with a beard – my wife says I will look very ugly.
Paul did encourage us and practiced this himself —
Even though I am a free man with no master, I have become a slave to all people to bring many to Christ. When I was with the Jews, I lived like a Jew to bring the Jews to Christ. When I was with those who follow the Jewish law, I too lived under that law. Even though I am not subject to the law, I did this so I could bring to Christ those who are under the law. When I am with the Gentiles who do not follow the Jewish law, I too live apart from that law so I can bring them to Christ. But I do not ignore the law of God; I obey the law of Christ. When I am with those who are weak, I share their weakness, for I want to bring the weak to Christ. Yes, I try to find common ground with everyone, doing everything I can to save some. 1 Corinthians 9:19-22