Knights Templars would have been seen by Orthodox
as other crusaders were, ie. as RC military aggressors. The Crusaders sacked Constantinople and expelled the Orthodox Patriarch of Jerusalem, replacing him with a Latin one. They were also in Eastern Europe, although I do not know how far east. Supposedly there is a 12th century fortress of the Templars in Srednee in the far west of Ukraine:http://ukraine.kingdom.kiev.ua/region/06/seredne_en.php
Putting aside those conflicts between Orthodox and Roman Catholics,
it is an interesting question how the Templars really compared with Christian teachings.
They were a monastic military order, which critics saw as going against the idea of monasticism. They also profited heavily from loans, which the Church's principles saw as usury - although the RC Church ignored this.
On the surface, there is alot of good things that can be said about them- they expanded Christian influence and helped keep Christian control over the Holy Land. They were dedicated to protecting pilgrims and making hospitals, and were dedicated to religion.
Their full name was the Knights of Solomon's Temple. So it would seem their goals and rituals would have something to do with Solomon's Temple. Yes, they occupied the area around the Temple, but it seems that there should be more than that. They had a secret initiation, and is that unusual for a monastic military order? This means there are unknown things about them.
On the other hand, there are some hints about them being heretical, but they are weak ones. First, the Templar leaders confessed to being heretics, engaging in deviant sexual and anti-Christian rituals. The problem with believing this is that the French king who tortured them into saying these things was severe against political enemies (like the Templars), expelling the Jews and Lombards, and using trickery in relations with England to take the English land.
Second, Templar castles and churches used gothic art and architecture which focuses on dark or even demonic themes. It doesn't make sense from a Christian perspective, but admittedly this was normal for the period. Third, there appears to be a link between the Templars and Masons, who have their own beliefs. However evidence for the link looks indirect.