The Eastern Orthodox Church does not appear on the radar of the esoteric Grail societies for one reason: No one in England, Scotland or France, in their formation of Grail societies, would view the Eastern Orthodox Church as the enemy. Their political and philosophical rival was the Roman Catholic Church, and that became the framework for the histories told by these Grail societies.
As an evangelical Protestant I am familiar with many strands of anti-Catholic propaganda. Because of my role as a pastor in a Bible-teaching church I occasionally receive, unsolicited and to my great misfortune, tracts and pamphlets detailing all kinds of hate literature from Conspiracy Theorists intent on smearing the Roman Catholic faith. One such claim, published by Jack Chick publications, states in comic book form that the Pope orchestrated the holocaust of the Jews. This is patently absurd, an insult to Catholics, to Jews, and to all who suffered under the Nazi regime, and an insult to the intelligence of any critical reader.
To my knowledge the esoteric Grail societies have made no such claim, and because they do not touch an issue as recent in memory as World War Two’s devastation, their claims might not evoke the same visceral outrage as do the claims made by Jack Chick Publications.
However, against the Roman Catholic Church the esoteric Grail societies make claims concerning the motivation of the Crusades and Inquisitions, events that were egregious in themselves even if more easily forgotten. All of this rests on the premise that “the Vatican” engineered the doctrines of Christ to fit some kind of chauvinistic, anti-woman agenda. Specifically, esoteric Grail Lore theorists stipulate that the Crusades were orchestrated to find the documents of the Grail Lore and destroy them. The Christ-descended Merovingian Line of France, robbed of its power by "the Vatican," would thus be deprived of its legacy as descendants of Jesus Christ as well.
Luckily for Merovingians, the Knights Templar got to the Grail Lore documents first. Unluckily for the Knights Templar, they ran afoul of the Inquisition in the early 1300's. Luckily for modern esotericists, the true location of the Grail Lore documents remained undisclosed despite the torture.
As you can see, the Roman Catholic Church presents an easy target around which to whip up conspiracy theories. We have already seen that the theories of the Grail Lore in its particulars: concerning the reach of Vatican power, the origin of doctrines for Christ's divinity, and the veneration of the sacred feminine, are not grounded in a working theory of history, nor are they grounded in a rational model of religious sociology. Where the Esoteric Grail Lore remains grounded, therefore, is in a stance of opposition to the Roman Catholic Church, a stance of bias and hostility.