Protestant countries in the Protestant League can declare war on the Emperor with the ‘Religious League’ Casus Belli at any time. This will drag in both Leagues and start a League War. A League War unlocks a new war-goal called ‘Religious Supremacy’. Enforcing this goal costs 50% warscore and can be enforced by either attacker or defender. If the Emperor wins and enforces the war-goal, Catholic is set as the official faith of the Empire, the Religious Leagues are disabled, and from then on all Electors must be Catholic (in addition to the Emperor). If the Protestants win and enforce this war-goal, Protestantism becomes the dominant faith in the Empire, the Emperor must be Protestant, and the Catholics become the opposition who may then attempt to declare war on the Protestant Emperor to reassert their control.
If the war ends with neither side enforcing their war-goal, a Peace of Westphalia event triggers that establishes Religious Peace in the Empire according to the principle of ‘Cuius regio, eius religio’, 'Whose realm, his religion'. This also ends the League Wars and removes the religious restriction on who can be Emperor. League Wars can also end if the opposition league - be it Catholic or Protestant - fails to declare war for too long. If enough time goes by without the opposing faith at least attempting to overthrow the ruling order, the Emperor will win by default and his now dominant religion will be set as official.