For me, I believe that Paul is saying that our goal is to share the Gospel with all people without prejudice towards their cultures or customs and regardless of their social or economic status in life. To do so means to enter into their situations without compromising the teachings of the Word and without a “I’m better than you” mentality. We are all,God’s creations and need salvation no matter where we are in life.
Where there is no clear teaching in scripture on specific issues we should try and be should try and accommodate our differences to bring them to Christ. Some would have different views on what could is allowed on a Sunday which is considered day of rest. We should ensure that whatever they believe would not actually be considered as a sin – going to the pub on a Sunday for lunch.
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.