TL;DR
An early sect within The Church of the Holy Mother made a pact with the patriarchy. This sect surrendered their claims to political power to the patriarchs and in return the patriarchs recognized the sect as the sole legitimate religious authority. As a result, having celibate, cloistered women running the church and working as advisors eventually became tradition.
luizpsr provides a great justification for the contemporary position of The Church of the Holy Mother: woman yield religious authority but let men take care of mundane matters. For my answer, I'm going to look into how this arrangement could come to be.
Side Note: My use of "church" as opposed to a "cult" is intentional.
Historical Examples in the Real World
Common Trends
If you look at the history of various religions (including Christianity), you'll see some trends:
1. After the initial emergence of the religion, a wide variety of interpretations and traditions develop and then begin competing to shape the religion's orthodoxy.
2. In order to spread, religions often adopt some values from the existing cultures.
3. Religious organizations often provide secular leaders with legitimacy and a good reputation in exchange for material support.
1 and #2 both explain why religions may seem contradictory; they aren't just the continuation of an initial revelation, but the on-going process of reconciling differing interpretations. #3, meanwhile, explains why religious organizations may compromise their ideological purity. In other words, a (nominally) matriarchal religion operating within a patriarchal society is not only plausible but realistic.
<PERSON> & <PERSON>
A specific historical example that is especially relevant involves the Christian Apostle <PERSON> and a woman named <PERSON>.
According to the Acts of Paul and Thecla, she was inspired by <PERSON>'s teachings to convert to Christianity and leave her fiancée for a life of celibacy. The stories depict <PERSON> enduring numerous trials - including miraculously surviving multiple attempts to execute her - before becoming a preacher. These texts also reference other female preachers and depict <PERSON> as an egalitarian and strong advocate for celibacy.
By contrast, the Pastoral Epistles depict <PERSON> advocating for women to serve a subordinate role in the Church and dedicate themselves to raising children. Though evidence is limited, it's likely this contrast was intentional. 412
The Acts of Paul and Thecla and the Pastoral Epistles reference people and events that are rarely mentioned in other Christian texts but promote opposed ideologies.
Despite Thecla being widely known and venerated until at least the 4th century AD, the Acts of Paul and <PERSON> did not become canon, but the Pastoral Epistles did. This suggests that those promoting traditional gender roles prevailed and became part of mainstream Christianity.
(This video goes into more details about <PERSON> and <PERSON>.)
History of The Church of the Holy Mother
Using the observations and examples above, here's a proposal for a history that would explain how The Church of the Holy Mother developed over time.
The Time of the Founders
Though the nation now has a unified political system and culture, in ancient times, it was home to a variety tribes. They differed in many ways, including gender roles; some were completely male dominated, others were completely female dominated, but most were somewhere in between. One of the few things these tribes did have in common was a prophecy in which a virgin woman would give birth to the <PERSON>.
The <PERSON> was born into a tribe that was effectively egalitarian. The people of this tribe were willing to accept a man as their leader, but also comfortable with the role <PERSON> would play. For while the <PERSON> was as wise, charismatic, and ambitious as his mother, he lacked her passion for theological debate and her skill with managing organizations. He dedicated his time to preaching to the masses, socializing with benefactors and allies, and eventually leading armies; he entrusted his mother first with organizing his fledgling religion and later with managing many domestic affairs of his burgeoning empire.
As a result, both the <PERSON> and his mother became influential and widely respected. However, the <PERSON> led a much more public life, leading to him being the better known of the two. Both his triumphs and failures were on display for the world to see, as were his virtues and faults; despite being revered, he was too human to convince most people that he was purely divine.
By contrast, the <PERSON>'s mother maintained an air of mystery. Her interactions with the public at large was limited. Instead, she was known through her writing - which she produced a lot of. This included letters communicating on behalf of her son, chronicles of her son's exploits, and treaties establishing the basic precepts and lore of the then-new religion. 72