Ukraine's Orthodox Church, which is powerful politically — Ukrainians tend to be more personally devout than Russians, who like to wax about Orthodox swords but don't actually go to church much — has explained that it rejects Western post-modern values but emphatically does not reject Europe or democracy.
Idiomatic? I don't think so. Looks like an imaginative use of phrasing.
My imagination brings up images of "sword-bearing protectors of Orthodox christianity". Maybe the word swords stands for "people who (in the past) took up swords to protect their faith, their Orthodox country". For "warriors", to put it simply.
So in a way the adjective Orthodox describes warriors. Russians wax lyrical of the past exploits of their Orthodox warriors, but attend churches less than Ukrainians.
Some distance before your quote, the article mentions a think-tank head who
..has transformed into a militant religious believer with Big Ideas and enthusiastic backer of Putin’s Orthodox Jihad.
So the idea of the article is that Putin wages an Orthodox Jihad, relying on the imagery of "Orthodox swords (warriors)" to fuel the zeal of the "volunteers".
I will lay odds that, ere this year expire,
We bear our civil swords and native fire
As far as France: I heard a bird so sing,
Whose music, to my thinking, pleased the king.
The story is old and repetitive, just replace France with Ukraine and civil with Orthodox.