I believe Paul is saying that in order to lead others to Christ, you must meet them at their level. We should not come with lofty words or attitudes that project cold arrogance. Instead, seek others by way of being relatable within their context. There are many ways to apply this idea to our Christian walk including: inviting someone to their favorite sport event, providing a meal when someone is sick or has had surgery, meeting up with people in their homes, asking for their advice in their field of expertise, etc. We should take precautions in that whatever we do, is not a stumbling block for the other person. It also goes without saying that we do not engage in any act that is immoral, illegal, or goes against Biblical principles.
Paul made himself a servant to win others to Christ. We learn that we don’t have to become a sinner to minister to others but to be at their level to lead them to Christ.