That's not the only reason by far.
King Charles was a very religious man who travelled throughout Europe and spoke with leading Catholic AND Orthodox people of his time.
He received a copy of the Alexandrian canon of Scriptures from Patriarch Cyril Lucaris, for example.
He also believed himself to be the head of the "Orthodox Church of England" as opposed to the "Puritans."
When appointing bishops, he always asked Archbishop William Laud to mark off the "orthodox" bishops with an "O."
And his theology leaned toward High Church all around.
There are Western Rite Orthodox who venerate him privately - and even publicly. Fr. Stephen Walinski of the Antiochian Orthodox Church in Omaha, Nebraska, had a beautiful icon of him written.