For God's smurfing sake
Final Fantasy X Cutscenes - Return to Bevelle - YouTube
"You've taken away the only means of calming Sin!"
"Preposterous! There is no other way!"
"And the only thing that could have pierced that armor, you have destroyed!"
Yes yes these are clearly all lies he's telling the party. He's obviously BS'ing them for one last grand performance to prove what an evil douchebag he is.
Or...MAYBE...he's telling the goddam truth and every goddam line in the game supports that this is what he absolutely believes?
Maybe?
Yes?
Okay.
Now that we've established Mika did care and was doing the best he could in his own way, let's examine the facts about defeating Yu Yevon.
Final Fantasy X Cutscenes - Help from the Fayth - YouTube
"I'm afraid your swords and magic won't be enough."
Now what are the odds the Fayth ever had a chat with Mika or any other Maester and explain this to them? To quote Ormi "zero, zilch and zippal."
It's not a matter of just whacking Yu Yevon with a sword or even blasting him with a cannon. As stated here and shown in the game, to defeat Yu Yevon you must repeatedly weaken him by having him possess summons and then killing those summons.
But ya know, fighting Yu Yevon is a pipe-dream to begin with. You know why? Because you're not gonna get through Sin's armor with anything less than the Final Summoning. The party only did as well as it did because Jecht had a connection to Tidus and thus he was weaker than he should have been. Any other Sin would have squished our heroes and their airship flat.
So to defeat Sin and Yu Yevon in the game, we had two entirely unique situations that had never happened in a thousand years.
So, no, I don't blame Mika and the others for believing their way was the only way. Until Tidus came along, there really was no other chance of permanently defeating Sin.
What's more, as Maechen said, the leaders of Bevelle were afraid of Sin, for good reason I'd say. They adopted those teachings to try and pacify Yevon.
Did they work? It doesn't matter. They were doing everything they could to keep people alive. If you cannot stop the abomination from crushing your home, why not grovel at its feet? You're not any less dead if he crushes you standing up or kneeling. Better to at least try something to save yourself and your loved ones.