Others might have already said this better than I’ll attempt to, but here goes:
Characters are meant to evolve. It’s boring as hell to play the same person through even 5 sessions of play, never mind dozens. For instance, I played a 3-year D&D campaign (3.5) where my character was a paladin. Despite liking the character, the only awesome thing he did was die to his nemesis and have an insanely cool death that allowed the party to kill said nemesis. He never really grew. MG and BW are about bringing change to the table. Shit will happen. Sometimes really potent shit. The job of the GM is to force that change, or give it a stage so the player can jump up and say “Fuck yeah. Here’s what I’m doing, and I’m a) backing up my belief and making it even stronger, or b) playing against it and setting myself up for growth in another direction.”
When a player is playing against a Belief, you have to feel it and so does he/she. It can’t be “Oh, I’m down on Persona. Gunna let you guys argue this out, but yeah… I’m like, you know, totally playing against my Belief by allowing that.” gets a Mountain Dew and checks email
It’s really an opportunity for character growth and change. My mouse had the Belief “It’s not about what’s right; it’s about what works,” making him a pragmatic and potentially off-the-Oath guard mouse. I had a lot of opportunities to change that, and I think I earned a Persona at one point for Moldbreaker, but I just kept building that because the other players had very noble Beliefs. I had to stand outside of that, I felt, to add some dynamism. However, I had originally chosen it because I wanted to change it at some point. What happens when what’s right really really matters? Will I do what’s right vs following my Belief? Possibly. Will that experience be enough to warrant a complete change of ideas/mindset? Not in my anecdote, but had we continued, I’m pretty sure it would have.
I find it’s hard to earn Moldbreaker without having a really solid and almost extreme Belief, which are my favourite kind anyway. It’s about the movement of the character within the game: is this the breaking point for that Belief? Does this situation necessitate or warrant breaking a Belief (which doesn’t mean re-writing it)?
No one is so static that they stick to their guns no matter what. Maybe Leon (from the movie) originally had a Belief that anyone within the parameters of the job was fair game, but he was forced to confront women and/or children who fell within that. “Oh fuck. Do I still follow the Belief, or is this a damn good time to alter it to reflect my issues with what the GM is pitting me against? Screw it. I’m changing it! I don’t kill them, and I’m re-writing my Belief.”
Having just re-read all that, I’m not sure I’m helping at all. Basically, it has to make sense. If it feels staged or disingenuous to you, deny the Persona. If it really feels intense and the player is forced to think about it, award it (and draw attention to it).