As @anon had quite wisely suggested, the best solution is having dieti(es) actively guarding true faith by divine intervention. However, the deities might not actually exist, or refuse to punish heretics magically. In this case, your Church (I am going to use Catholic terminology, since, like it or not, it is the longest living and greatest centralized religious organization on the World.) needs to rely on mortal methods.
Others suggested, that you should have a liberal, decentralized, polytheist mythology. This really helps if you only want to avoid 'open schism' (priests saying to each other: You heretic are going to burn in the Hell!), but would encourage regions to 'like' different gods from the same pantheon , and worship them above the others, or to develop fundamentally different interpretations. So if you really want your people to believe in the same things, you are going to need a centralized church.
1.) Have one leader Your Church cannot allow endless disputes on synods. It needs a pope, that, after hearing the arguments, finally decides what is Right.
2.) Travel a lot If the religious leaders of each region stay there infinitely, they are going to loose contact with the other parts of the Church, and identify to much with their province. Ideally, even your 'pope' should be in constant motion, visiting local communities one after another, like the apostles did in the early days of Christianity. They would use both the portals, and conventional means of transport in-dimension.
3.) Become integral part of the society The real cause of the influence of the Church was not it's centralized power, but its omnipresence on every level of everyday life. It stood on the side of the kings, diligently writing down his edicts. It regulated the lust and greed of the lords. It stood by the cradle, marriage bed (not literally) and dying bed of the burgeon. It celebrated together with the peasants. It maintained hospitals and schools: the priest did almost all the intellectual work. Wove the structure of your Church into the structure of society, so that everybody benefits from it's functions, not only the warlords and merchants using the Gates.
4.) Don't let secular powers interfere Often in the medieval times kings tried to nominate bishops themselves, and 'revolted' against the pope, refusing to proclaim his edicts. Other times they held back church taxes, or did not appoint bishops for a long period, letting their secular gubernators collect the incomes of the bishopric.
Often even the papal throne became a subject of power struggle between kingdoms or the powerful families of Rome City, leading to anti-popes. Not to mention when the King of France forced the Pope to move into Avignon, and live under his influence: https://en.wikipedia.org/wiki/Avignon_Papacy
Such events would mean a huge loss of face to the Church, so you have to hold the secular powers firmly in hand.
5.) Do not abuse your power You want your Church to be a moral authority. This does not mean that you need the maximal amount of direct secular power. If you raise the taxes to much, depose to much popular monarchs, or your priest do too much rotten things, your moral authority will sink, leading to people finding answers to their thirst after God elsewhere.
However tempting the immediate benefits of power, wealth and pleasure may be, your clergy should avoid making itself loathsome and loosing credibility.
6.) Learn to change while not changing The personal and social needs which are to be satisfied by faith change over time. While keeping the dogma strictly, your Church needs to speak to the people in different ways, shifting emphasis from one part of the teaching to the another. The leadership should carefully balance, whether a given theological direction, local movement or belief is outright heresy, or is, although using different 'tone' as the mainstream Church, useful and eligible. Ecclesia semper reformanda est
7.) Support multiculturalism Your Church is to work on a lot of different cultures. It has to do everything to slowly and peacefully mold them together. Send priests from culture A to culture B, organize pilgrimages, and regularly hold a great Event (like the Olympics in the ancient Greece) where not only the clergy, but a significant part of the simple believers would come together, to glorify the gods, while also doing something fun.
Wisdom and Luck Some of the above points are contradictory: How should the priests maintain living social ties with Everyday Joe if they are constantly sent to foreign cultures? Where is the line between holding back an aggressive dictator and abusing your power? The Church needs wise, blessed and quite saint leaders to decide what is good for the religion, which as little self-interest as possible.
+1) Have an enemy Have a small but noticeable fraction of your people follow a radically different faith. Not some petty heresy to which is easy to convert and back, but something sinister, abominable and unholy, like satanism. If this bad religion is the only alternative in the mind of the people, they will rather stick to the orthodox teachings.