What's the noun for ministerialists? Here's the word you're looking for.
ministry
Government department, at the administrative level normally headed by a minister (or equivalent rank, e.g. secretary of state), who holds it as portfolio, especially in a constitutional monarchy, but also as a polity
The complete body of government ministers (whether or not they are in cabinet) under the leadership of a head of government (such as a prime minister)
“But, for the most part, of the youthful sons of the churches, the right and best men do enter the ministry.”
“Next year will mark fifty years of evangelical ministry at the church.”
“In the decades that followed his death, out of the circle of 12 that had accompanied him during his three years of ministry, 10 would die a martyr's death.”
minister
A person who is trained to preach, to perform religious ceremonies and to afford pastoral care at a Protestantchurch.
A politician who heads a ministry (national or regional government department for public service).
“Sur la question relative a la preservation de l'exercice du droit syndical, la ministre a affirme que ce point est inscrit dans le document.”
“Abordant la regulation du marche, le ministre a indique que cette exigence necessitait la realisation de marches de grande distribution.”
“Le ministre a ensuite precise que les objectifs de ce projet de loi resident dans la volonte du gouvernement de reorganiser et d'actualiser le regime de la copropriete.”
“The faithful servants of God in public life are his ministrants as truly as those who perform the divine service in church.”
“He had merely stated the condition in which the ministrants then were, and in which they should remain.”
“This vision set in motion a train of visitations by angelic ministrants directing the young prophet in the process of restoring the gospel of Jesus Christ.”