I think it has a great deal to do with America’s English heritage. During the 16th and 17th centuries, England and Spain were enemies. England had recently become Protestant, while Spain was still very much Catholic. My understanding is that there was a great deal of anti-Catholic propaganda in England during this time. Plus, the Church of England became identified with England itself, and Catholics were viewed as a threat to the state, not simply to the Church of England. Spain was a serious threat at this time, and perhaps we would be living in a rather different world if their armada had been successful. However, Protestant England (with the help of the weather, I believe) defeated Catholic Spain. The fear of Catholicism was transmitted to the English colonies. The old conspiracy theories and exaggerated reports of Catholic atrocities (such as vastly overinflated reports about Inquisition-related deaths) became popular in America, as well. These beliefs about the Catholic Church have been passed down throughout the past centuries, and are particularly strong in certain Protestant denominations.
By contrast, there is no strong historical basis for English Protestants and their descendants to have any kind of fear of Orthodoxy. Orthodox Russia or the Orthodox Byzantine Empire were not threatening English sovereignty, so American Protestants don’t have an inherited bias against the Orthodox faith. So, while Orthodoxy holds to nearly all the doctrines of Rome, Protestants know very little about Orthodoxy, and so they have no incentive to strongly oppose it.
As Protestant missionaries move into historically Orthodoxy countries, they have begun to form arguments against Orthodox theology. Not long ago, I read a Baptist pamphlet about evangelizing Orthodox Christians, for example. However, even that was not full of the kind of hysteria that is often found in anti-Catholic literature.
.
