[Kairos is time as the right time and Chronos is time as the time of day.]
Rector, to make your point, which surely is salutary, perhaps a more specific and less hyperbolic, fact-eliding means is available. I refer to differentials between taking time as Kairos and taking time as Chronos, a discussion with which I am sure you are familiar.
The Church (Greek and Latin) takes time as Kairotic more than as Chronologic. Both aspects of time are of course always present. However, The Church -- because of The Bible and The Fathers (Greek and Latin) -- emphasizes time as Kairos in affairs of soteriology. This is the proper emphasis.
The Orthodox (Greek-Russian) Church has been far better than The Latin (Catholic-Protestant) Church at maintaining awareness of time as Kairos more than of time as Chronos. Such awareness comes with the natural emphasis of The Church on soteriology.
I believe that by Oligarchy you reference those who treat time as exclusively Chronos -- they are by definition therefore outside The Church -- and that by Patriarchy you reference those who treat time as most importantly Kairos, albeit without denying time as Chronos. Such are by definition therefore inside The Church, whether their outward title is Moslem, Jew, Christian, Hindu, Zoroastrian/Baha'i, or anything else, including even Atheist, although few Atheists grasp time as Kairos.
The Orthodox Church has performed far better than The Latin Church in adhering to The Church's preference for taking time as Kairos, albeit while also affirming time as Chronos.