I think there should be a differentiation between countries in the respective Leagues (full war participation, limited to christian nations that have the fitting state religion) and supporting countries from the outside. Historically Sweden, Austria, Spain and most of Germany would have made up the Leagues, and the Ottomans, Poland, Russia and France could be considered outsiders who took sides to strengthen their own position, but not due to religious reasons.
Now in EU4 obviously the composition of the leagues could change drastically from game to game, and that's great. But I don't want to see Ottoman or Russian armies running all over central Europe, with the historically important forces being sidelined to watch in awe. Add a "support League" button for nations that don't fulfill the religion requirement to join, and let them outline the support they offer ("20 Ducats a month and 50 regiments as condottieri for 5 years to the League leader"). The League leaders can consider this support in their decision to go to war and get control over the offered armies. If an outside country wants to actively participate, it has to declare on its own, opening a second war with all it's consequences.
Now in EU4 obviously the composition of the leagues could change drastically from game to game, and that's great. But I don't want to see Ottoman or Russian armies running all over central Europe, with the historically important forces being sidelined to watch in awe. Add a "support League" button for nations that don't fulfill the religion requirement to join, and let them outline the support they offer ("20 Ducats a month and 50 regiments as condottieri for 5 years to the League leader"). The League leaders can consider this support in their decision to go to war and get control over the offered armies. If an outside country wants to actively participate, it has to declare on its own, opening a second war with all it's consequences.