This would be more difficult (ok maybe a pain) but would it make more sense to have a secondary CB? If they conquer say... Kiev and Constantinople a global event fires (Conquerer of the world or something). When that flag is set they have access to the secondary CB which allows attacking Christians. This way the AI could (theoretically) have it to, but there would be and intermediate step. Though I freely admit I have never tried to mess around with a CB and a global flag.
Though from a player perspective I would prefer to just run wild without the restriction.....
Player should get to do whatever they want with the Mongols, yes. It's a sandbox game still here, after all. Mainly, we want to make the sandbox players are in actually act like a sandbox and not a pathological house of horrors. That's what historical plausibility's really about: since it's a game with a historical setting, the historical part comes into play. But the key is the plausibility. So we want to guide the AI and tweak the crap out of everything generally such that, if things are left alone (or the player were to choose to role-play history by the book for some odd reason), the outcomes are actually believable (though hopefully still quite varied-- a history book is very believable but not a lot of fun with which to play).
That said, yeah, the best way, in practice, to guide the AI Mongols is quite a bit more detailed than simply disallowing attacking christians (or, apparently, it's just Catholics, which is Much Better though still IMNSHO something that eventually should go). Given time, I would craft the Tribal Invasion CB (or, in non-Mongol cases of similar AI-guiding, I might actually use a separate alternative CB altogether to keep the special-case logic from clogging up the vanilla CB) differently:
I'd first draft out what I believed to be a set of perfectly reasonable paths of conquest they may have taken
with that CB, should the right opportunities or conflicts have arisen to change history. I'd draw out the very farthest I could see them realistically conquering along all of those vectors without certain obvious factors limiting their ability to further scale without adaptation. That adaptation implies losing usage of their special conquest CB; that is, successful and stable integration and rule of their conquered realms implies that sustainable rapid conquest no longer applies (i.e., adopting a semi-universal legal system, a concept of claims to land, etc.). So we're really drawing the max conquest vectors out
for that particular CB, keep in mind. It's still plausible for the Mongols / whatever group we're balancing (e.g., Imperial Reconquest is a parallel) to expand in other, more traditional ways, ceteris paribus.
Then I'd figure out the most concise and flexible way to encode those tiered zones of conquest with the CB with logic based upon any number of factors. Meneth simply chose to make Catholics not an option. I wouldn't do that, as they should be (esp. if the catholic schism has been mended) and there's nothing fundamental about Catholicism that would prevent the Mongols from invading, so one has to be careful with building stopgaps out of correlations with territory. It's just a placeholder for a territory-based conquest-zone-tier qualification system, and I think in this case, it's entirely plausible (as in, 1-3% of the time they successfully invade at all, sure) for the Mongols to pose a threat to the HRE directly and completely conquer the Magyars. This would also be a lot more fun to potentially face rather than knowing they'll never get into Hungary because... well, Hungary follows the views of the Roman Catholic Church. It just requires work. And a lot of things do, so sometimes stopgaps, even really super rough ones, are appropriate.
Global flags might be a perfectly good way of building such a tiered conquest-zone qualification system. Only a few would be needed in this case. And, yes, they're common to use in CBs for stuff precisely like this.
Nevertheless, the change I'll add here at some point shortly is only going to disable the catholic check for the player, because the Mongols are behaving reasonably well currently (other than never proceeding into where they historically did-- epicly so, and fell apart thereafter-- and stopping just short of it due to the current logic), and thus, it's not a very high priority. However, it IS a high-priority to not impose such weird restrictions that are only based upon happenstance and not the actual factors which limited their conquest upon the player. The player can damn well decide to skip Russia and bee-line straight into Hungary, Austria, and straight to Franconia if they can somehow pull it off and not lose everything shortly thereafter.