People who think they've found the best spiritual path have a right to proselytize, but sometimes it's kinder to refrain.
One more factor complicates this picture. It is that these Orthodox lands have just emerged from decades of oppression and persecution. As the USSR cracked down on institutions at odds with state-sponsored atheism, some 20 million died in Russia alone. Brave Protestant missionaries like Pastor Richard Wurmbrand tried to tell Westerners this at the time. American response to this persecution was weak and confused because it was hard to see what, in practical terms, we could do; also, due to Cold War prejudice against Russians, the fate of Russian Christians did not seem pressing.
During this persecution, the church in these lands was severely depleted, to an extent we cannot imagine. Most of its leaders were killed, in horrible ways and huge numbers; 40,000 Russian pastors were killed under Stalin, so that at the end of his dictatorship only 200 remained. Churches were desecrated, possessions confiscated, and the faith was openly and officially attacked. One young Russian woman recently told me she grew up hearing, "Study hard, or else you'll be stupid, and then you'll turn into a Christian."
As that miserable time recedes, the Orthodox Church is severely crippled and in desperate need of support to rebuild. But most outreach to these lands has not been to strengthen what remains but to establish new, separate churches. To the Orthodox, this is cruel. They feel like what the communists started, Americans are bent on completing: the destruction of their cherished faith.
Moreover, it seems to Orthodox that Americans have unfair advantages, stirring up more bitterness. American financial resources are huge compared to that of the diminished Orthodox church. While Orthodox churches are still impoverished and in shambles, new Protestant churches can look as nice as new American churches. Also, since anything American is "cool," the church struggles against another frustrating disadvantage: the perception that it's not fashionable, while the incoming churches are.
So what can Protestant missionaries do? Go to formerly communist lands and seek out those who have held the faith through years of great danger. Perhaps we Westerners, who have never been tested by such persecution, can learn something from so heroic a faith.
Ask how you can help them rebuild. Prison Fellowship has set a good example by partnering with Orthodox chaplains rather than establishing a separate parachurch ministry. I've heard others talk about working with Orthodox leaders to develop Sunday school materials. There is no doubt that the Orthodox Church can use refreshment and revitalization, which come so naturally to Americans. If Protestant missionaries believe that Orthodox Christians are fellow members of the body of Christ, working together fulfills their mission just as well as working separately.
But some Protestant missionaries might not feel that way. They may believe that Orthodox are not "real" Christians, and that the Church should die. This could be due to ignorance about the tenets of Orthodoxy, or a mistaken presumption that it is the same as Roman Catholicism. Not everyone is trained as well as they should be. One Protestant missionary to Russia lectured me that "anybody who prays to icons can't know Jesus as Lord," showing that even after her trip, she still did not know that Orthodox don't pray to icons.
Yes, it is your right to proselytize, and you are not obligated to care about any of this. At least be aware of these factors, however, so you can make decisions in awareness of "the law of unintended consequences." The dilemma is summed up by a missionary T-shirt a friend of mine observed. It read, "Bringing the light of the Gospel where it has never shown before." Below this there was an image of a church with onion domes--topped by crosses.