The final end of the State isn't the "protection of liberties," but the common good, since the protection of liberties is justified as being good for the individuals in society.
Your position is self-contradictory and incoherent, but I give up on trying to convince you of that fact.
moralistic statists who seek to guarantee it equitable outcome.
The State, then, exists to help man to temporal happiness the Church, to eternal. Of these two purposes the latter is more ultimate, man's greater good, while the former is not necessary for the acquisition of the latter. The dominating proximate purpose of man must be to earn his title to eternal salvation: for that, if needs be, he must rationally sacrifice his temporal happiness.
Does that sound like "guaranteeing equitable outcome"?
Yes -- that is precisely a statement that the outcome of moralists (people behave in accordance to the moralists' preferences, by force if necessary) is to be guaranteed.
However, all they may legitimately seek is opportunity (the state protects their right to live as they wish, and to communicate their arguments in favor of imitation by others).