Time will tell on this. Maybe it wasn't in the church's interests, maybe it was. We'll see. He certainly was sincere. But the idea of Terran as an "undeserving city-state" is a purely subjective and political assessment. Undeserving... by what standards? What possible standard could you be appealing to?
Standards on the worthiness of being protected were given and agreed by for a good number in the early days of the crusade. Further, worthiness can be measured by possible gains versus costs. Sure, the church gains a new limb... but it wounds itself at the core for it.
The issue of engagement is a real one. As I see it, most of the most engaged Astroists are on the periphery. Many Astroists in theocratic realms are just kind of along for the ride, while the people who really invest in the faith are out being missionaries (there are exceptions, obviously). Mordaunt should have done more.
But that's not at all a problem of the church overstretching itself or something, or a fundamental lack of appeal of the church. That's a few personality mismatches. Reshuffle the cards for the next hand, and things will shake out differently.
Also, people keep talking about the state of the church: lolwut? We just won a crusade without fighting a battle. We literally just had a practically bloodless victory, added a theocracy, several new converts, and seem to, as best I can tell, have lost absolutely nothing. Oh no, people are angry! So we'll have to play to those peoples' interests in the next round.
I think the idea of this conflict as the great schism in SA is shortsighted and erroneous.
You really exaggerate the earnings and ignore the costs. A great "victory" of gaining three poor regions, a handful of political converts, at the cost of great internal and external dissent. That's not just the few nobles who really criticized the church persistently, like Jonsu or Gustav, it's all those who agreed with them without wanting to publicly oppose the prophet, but who now see the church as being a political tool for the elders (like Hireshmont's, because it doesn't matter what his true intents are, the appearance of it being for political ends is too great), and who will not feel themselves as blinded to actually obey. They will be more open to side with national interests in church disputes ("Remember that time where an elder just called for a crusade for his own sake? Why serve the Church when the Church serves another?"), they will be less inclined to encourage non-faithful to adhere ("Oh, if you join, you might be forced to go on stupid wars to further the elders' personal aims").
You've "practically bloodless victory"? What's the worth of another theocracy if nothing's to compel them to actually obey the church. What's the worth of the new converts if their sole purpose was to be able to lobby in their own interests, against current policies? People are angry, yes, but that's actually worth a lot more than what was gained. You can't just rotate "Oh this time we piss these people off, next time we give them a cooky, then rinse and repeat". It takes a darn lot of cookies to make people you pissed off forgive you.
No, we didn't naively assume all the faithful would be eager. We correctly assumed we would win. And behold, we were right. Right as complaint was reaching a fever pitch and proclamations about how the crusade would be expanded as a political tool... peace was signed. Barely a battle was fought and the war was done. The church managed to flex its soft power without even a declaration of war.
Did we expend some political capital? Sure thing. So now we enter a rebuilding phase. Decisions always expend resources. This one maybe a large amount, so we'll have to do some real work to rebuild. But we're rebuilding from a broader, stronger position than previously.
It's not just perceived as a political tool to save Hireshmont's city, but also as a last move done out of spite against Phantaria. And that, no amount of stepping down and leaving the realm will change anything to. Time will indeed tell who is correct, but I don't see the church as being in a "broader, stronger position than previously". I see this as structural damage. From what I've seen, the Church overextended itself, and have damaged its internal cohesion to do so, and will never be able to properly heal this gash, merely patch it as best it can.