But that's not necessarily what the "League" mechanic tries to simulate.
"Leagues" in the game sense aren't the same thing as the formalized historical entities of the Catholic League and Protestant Union (which wasn't all that cohesive to begin with) - or even for just the major political players (France, Sweden, Austria, etc) for that matter - but more of a catch-all for all belligerents in the wars.
What are "the wars"?
This is where the problem appears. You're using a very wide definition of the Thirty Years' War which makes it appear more cohesive than it was in reality. Imagine an alternate history in which Muscovy attacks Sweden in 1634 in an effort to take Livonia - perhaps the Habsburgs might try to encourage them to fight harder or send them some sort of support. Does that mean that Muscovy has intervened in the Thirty Years' War? Of course not. Muscovy is attacking Sweden for its own reasons and with its own motives. It's going to stop attacking Sweden when it stops being convenient for it to continue. It has no special attachment to the Catholic cause. It's making use of the opportunity.
The Ottomans are the same. If they attacked Austria they might receive encouragement and support from France. But are they really intervening in the Thirty Years' War as such? Are they really taking up the Protestant cause? Of course not. They don't understand the nuances of HRE politics and European diplomacy. They and the Protestants might try to use one another as tools to achieve their mutual goals, but they have fundamentally different attitudes toward the conflict. The Ottomans aren't in it to the end, determined to bring down the Habsburg giant. They're just looking to use the opportunity to push forward their border in Hungary, and will drop out of the fight when it's convenient for them. Just like Muscovy.
Their war would be fundamentally separate, even if they may share some of the same enemies.
Now you can take a position like "every potential war involving a member of the Holy Roman Empire during that period is part of the Thirty Years War," but if we go with that then we give up on the possibility of making the Thirty Years' War anything special. And everyone complaining about the Ottomans joining should be told not that it's realistic (it's not), but that the leagues are just a contrived way to create a massive war and aren't all that connected to history.