On talking to my non-Christian friend about religion, his argument was how can he accept a religion that does not accept him. Of course, he knows that he cannot marry a Copt because of that matter. I want to draw him to Christianity in any possible way. What do you think I should do or say to him?
The approach you need to take when talking with any non-Christian is how we as Christians, and our Coptic church accepts everyone with a loving heart whether or not he chooses to commit his life to Christ. There is a difference between acceptance and membership. Acceptance comes from love and friendship, not by partaking of the Eucharist. It comes from kind acts and complete explanations to his questions. No church in the world invites non-Christians to take communion when they do not believe, because it is a church duty to keep the integrity of this Mystery and reserve it for people who truly want to be a part of our Lord Jesus Christ and confess His death and resurrection.
When we evangelize to non-Christians, we should first talk to them about God and His love for us. About the great sacrifice that our Lord Jesus Christ offered to us on the cross. Get them to accept our Lord Jesus Christ and Christianity before going into Orthodoxy and the church sacraments and rituals. After you gradually show them love and acceptance, draw them to attend Bible study in the church, you can invite them to attend the liturgy and pray always that their ears and eyes be opened that they may see the glory of God and long for joining the church.
For more information, check the evangelism website and also check the other Questions & Answers on evangelism.