Good Post, SV.
Also, I would add that God did say "For the other gods are deamons".
We as Orthodox Christians cannot truly pray with members of other religions, because they do not pray to the same God as us. God makes it clear that all is lie but He. The faith cannot be compromised in the name of good relations with others. We love them, but loving does not mean accepting false beliefs. They show good behaviors and values, which is proof that God has not left them empty. Yet they do not know who the real God is, and it does not help to be altruistic. Our love comes from Love's Source: God Himself. All other semblaces thereof are not pure, true love. So, if we pray with others of other faiths, the question comes up "Do they understand love as God show it, or, are they praying for a mere semblance of love? " Or another is "What are they praying for exactly?" And since they do not pray to The One God, they must be praying, deductively, to either the wind or to a deamon. It may seem cruel, but the truth is often harsh. We may pray to God for them, but not with them to other "gods".
Also, pertaining to other Christians, many outside the Church have adopted the apostacies that the Holy Church as a whole had rejected. St. Paul writes "Shun those who walk disorderly among you." Their understanding is tainted with a falsehood that we as the full Church Unchaged cannot accept. It is basically (though WAY oversimplified) like a railroad man buying a railcar that he knows has a faulty wheel. In the case of the Roman Church, there are things, such as Papal infalability, the Emaculate Conception, Culpulsatory Celebate Priesthood, use of Azyms, and Papal Supremecy, that we see as "bum wheels" that we cannot place on our train, lest it be lead off the track. Again this is said in love, and not out of spite of my Roman Friends. That is why we say, "let them come back the same way they left" so that all runs as it has from the beginning. Anything else changes the faith, and we dare not do that.