How do the other branches of Christianity regard Eastern Orthodoxy?

[GMantis]

 While I'm atheistic, I come from an Eastern Orthodox background and feel cultural affinity with the church, so I've been quite interested in this question.
The attitude varies greatly. There are some fundamentalist protestants who regard Eastern Orthodoxy as idolaters, but I know much less about the opinion of mainline Protestants. In any case, I don't think they have much respect for the Orthodox church, considering their aggressive missionary campaigns in countries with a predominant Eastern Orthodox population.
I've heard that in their beliefs the Lutheran church is somewhat closer to Eastern Orthodoxy compared with other Protestant branches, but I can't confirm this.
The Catholic Church is pursuing reconciliation, but as it's reconciliation on their own terms (ie swallowing Eastern Orthodox Churches) they are unsurprisingly getting a rather cool reception.

[GMantis]

American Protestants have zero understanding of Eastern Orthodoxy.

Generalize much?

What understanding do you have?

[GMantis]

I'll throw in one thing that is probably untrue. 

At one point, I considered joining one of the Orthodox sects...largely because their theologians are intellectually strong and their liturgy is so beautiful.  I opted against it because I am committed to the ordination of women and other doctrinal differences.  But I maintain a deep affection for both Roman Catholocism and Orthodoxy.

So when I mentioned this to a Greek friend, she said..."Jim, you would always be a welcome guest in an Orthodox Church.   They would treat you really well.  But you would always be a guest.  Your name needs to end in "opoulos" to really be a member."

She was overstating, but suggesting that no church is quite so culturally closed.  I wonder if that is really true. 

If there is such a thing, I think that applies only to the Greek Orthodox Church. There are multiple Orthodox churches, which are completely independent. Still, I don't remember the Bulgarian Orthodox church attempting to proselytise (not that it would be competent enough to actually proselytise...).