I don't know what the official position of the Church is, although I did hear something along those lines. I do know that, like all rules, we sometimes have to use our common sense about interpreting them in the interests of being kind--you know, being a Christian. We often have social obligations that don't fall into neat compartments. Err on the side of love.
My personal decision would be to 1) try to avoid such situations, but, if they happen, 2) participate insofar as I am able because they are my friends and I would not willingly hurt, nor make a big deal about religious differences, with a friend. Unless they are doing something in their prayer that's wholely anti-Orthodox, I would try to compromise with them. I might even say--without ostentation--a silent Orthodox prayer instead. (If they spontaneously decide to pray, they're probably pretty nice people to begin with. Obviously, they're not axe-murderers.) Do you mean to tell me you'd let a perfectly good opportunity to pray to God to pass you by?
If, for some unavoidable reason, I ever end up in a Protestant church, I'll be gracious and good willed. God still hears your prayers.