Scripture points out that anyone who believes in Jesus Christ and calls out to Him will be saved. The scripture does not distinguish between Greek (Gentiles) and Jew. In today's modern world this teaching could be extrapolated by remembering that it also does not distinguish between Eastern Orthodox, Protestant, Roman Catholic or any other believer, anyone who calls out to Him will be saved regardless of their religious background.
Interestingly, while both the Eastern Orthodox and the Roman Catholic churches have similar traditions, there are some marked differences when it comes to certain Church teachings and traditions. Notable among the beliefs and non-beliefs are Papal supremacy, Hell; is it a place or condition, the Immaculate Conception, the Filoque to name just a few. The question might be asked, do these traditions and their acceptance or rejection affect a person' salvation? The answer is No for as St. Paul professed in the book of Romans, "Everyone who calls on the name of the Lord will be saved!" Romans 10:13.
Perhaps another piece of scripture from St. Paul that is also worth contemplating and remembering is, "Don't have anything to do with foolish and stupid arguments, because you know they produce quarrels" 2 Timothy 2:23. No matter what the tradition may be and while it might be interesting to discuss how differences in traditions arose, do not let them become a stumbling block to one's faith, Christ is not exalted by discord and "foolish and stupid arguments".
Central to any discussions is remembering that they have no bearing on a believer's salvation. Orthodox Christians have been taught by the Holy Fathers that their salvation is based on their on-going faith and relationship with our Lord and Saviour Jesus Christ.