I keep holding out to my hope that one day we'll discover that quantum mechanics isn't the full picture and that the universe is actually deterministic at some fundamental level, since that makes more sense to me intuitively, but I readily admit that I believe scientists when they say there are really good reasons to believe that quantum processes truly are random and there are no hidden variables. But, I'm getting philosophical and off topic to an extent.
This does bring up a few things to contemplate though. For one thing, it brings up the question of how much like a computer a brain is, since as you say you can't program randomness into a computer. If brains fundamentally work the same way, that means there's no randomness to our behavior and it's all dictated by solid rules that at least in theory could be defined and used to predict behavior perfectly. In practice it would be so insanely complex you can't do that, but I think it does have some merit in religious discussions to consider that as a possibility since it kind of means you're not responsible for anything you do. There's some wiggle room there for sure, but I mostly mean it in the context of things like eternal reward or punishment for religions that believe in that. If you're predestined to do something from birth, how can you be blamed for it?
And of course that goes back to things like Christianity where God presumably does know precisely what you're going to do before you're even born, since he presumably knows everything, including the future with perfect accuracy. If you believe that, and also believe in things like eternal burning Hell where you're tormented forever, how does that influence your feelings on God? I know that predestination is a big religious topic but it's not one I hear discussed in person. I think most people around here, who do believe in eternal punishment for dying as a sinner, prefer to just sweep it under the rug and believe in free will anyway without scrutinizing it at all. God can just make that work for them somehow I guess, like making a rock too big for himself to lift it and then lifting it anyway.
Then, circling back to the nature of randomness in quantum mechanics, you could argue that our behavior is modified by that and isn't subject to harsh rules. Sure, that may even be true. I don't know how much that actually applies to the chemistry or electrical excitations in our neurons, but I can believe that it could manifest some macroscopic changes ultimately. But... if it's random, is that any better than being governed by rules? You still have no say in the matter. It's random.
You could then try to argue that that's where your soul comes in, I suppose. Like God set up the universe in such a way that our souls are manifestations of some kind of driven bias in quantum mechanics that gives us agency. That's impossible to disprove, so maybe it's true. But even if it is, it doesn't sidestep the issues I mentioned above about God knowing the future and what you're going to do, which in a sense means you still have no choice in what happens.
I guess if you don't believe in an all knowing or all powerful God then the problem is less serious.