Question: "Is it proper to say "Memory Eternal!" in reference to the non-Orthodox?"
When we sing "Memory Eternal!" at a funeral or a pannikhida, we are not praying that the memory of the departed will be eternal among those here on earth, but that God would remember them eternally. Of course, by this we do not mean to suggest that God might forget if we don't ask him to remember them. We are speaking of a particular kind of memory.
In the Gospels Christ tells us that on the day of judgment, many will be surprised to hear the words "I never knew you: depart from me, ye that work iniquity" (Matthew 7:22-23). And in the Scriptures when it speaks of "knowing" someone, it refers to the intimate knowledge that results from relationship, and so the point in this passage is that while the people in question professed to be followers of Christ, they did not have a real living relationship with Him.
When we pray that God would make the memory of the departed eternal, we are also alluding to the prayer of the wise thief on the Cross who said to Christ: "Lord, remember me when thou comest into thy kingdom" (Luke 23:42).
When considering whether it is proper to say "Memory Eternal!" with reference to someone who is not an Orthodox Christian, you should consider whether or not it would be proper to do the funeral service or a pannikhida for them. And the answer is "No." It is true that there is a very short order of service for a non-Orthodox Christian that can be done if they such a person has no one to bury them from their own faith, such as might happen in an Orthodox country. But such services simply consisted of singing the Trisagion, without any of the other prayers of a funeral or pannikhida, including "Memory Eternal!" And if we are not permitted to sing "Memory Eternal!" even at the burial of a non-Orthodox Christian under such circumstances, we should not say it with regard to them in other contexts either (see: On the Burial of the Heterodox).
We certainly can pray for them in our private prayers, and we do not preempt the judgment of God, and assume we know what it will be in their case, but "Memory Eternal! is a prayer that should be limited to baptized Orthodox Christians who have at least not renounced the faith in this life.
Update: St. John of Shanghai did allow "Memory Eternal!" to be sung, along with some other hymns, as "an exception for those persons who during their lives demonstrated goodwill towards the Orthodox faith and took part in its life to the best of their abilities..." It is not clear exactly what sort of person would fit into that category, although perhaps someone who had an interest in conversion, but had not yet completed the process would be such an example. But clearly, saying "Memory Eternal!" for those who had no connection with the Church would not fit, even as an exception.
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