The answer
Although the Coptic and the Greek Orthodox Churches have agreed to accept each other's baptism, they still are not yet in full communion. A baptized Greek Orthodox has to receive the Mystery of Chrismation in the Coptic Orthodox Church to become a member of the church and be allowed to partake of the Holy Communion or to marry in the church.A person baptized in the Protestant Church is not baptized in the Orthodox faith i.e. does not accept the mysteries, the position of St. Mary in the Church, the intercession of the saints etc. This baptism is not accepted in our Coptic Orthodox Church and therefore he/she has to be re-baptized.
Answered by His Eminence Metropolitan Youssef (opens in a new tab)