Disestablishment of State Religion refers to the partial or full removal of National or State sponsorship of religion.
Throughout history, States have adopted, or sponsored religions. State sponsorship has varied from full Theocracy, with the State existing to promote a particular religion or sect with religious doctrine given force of law, to active promotion of no religion. (Many Liberapedians are Atheists but as Liberal we don't think atheism should be forced onto people as happened in Totalitarian Communist Countries like the USSR.)
State sponsorship of religious/nonreligious doctrine has, and continues to create extreme conflicts between the Official Doctrine and those who do not practice the Official Doctrine (Dissenters/Schismatics/Heretics/Heathens/Infidels/etc.). Tolerance/intolerance for religious dissent places dissenting minorities in a position varying from a sort of benign neglect to outright hostility where dissenters are subject to the most extreme punishment imaginable.
The compromise which Liberals have devised and promoted to maximize the liberty of all people and protect the lives, property, and rights of all people (including dissenters) is disestablishment. Disestablishment is not a perfect solution, and is always going to be resented by some within any society, but it does cut down on oppression, war, slavery, murder, rape, torture, forced conversion, and all the worst aspects of societal behavior.
Sometimes even the most tolerant people are challenged when faced with the intolerance which seems to arise from within groups dedicated to a particular doctrine. Perhaps the best we can hope for is that people of good will attempt to constrain those inflamed by passion from inciting mob violence.