For religious/spiritual folks: How compatible are scientific principles/theories with your beliefs? How have you struggled with any conflicts between the two?

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Good question, and the answer is there's no contradiction and I've never struggled with a conflict. Unfortunately, most people who are aware of / care about science buy into science's claims (yes, I know science technically isn't an entity that makes claims, but for certain practical purposes it is) that there's no such thing as a soul and such, but none of that is proven or even provable by science. It's a part of the physicalist and mechanistic worldview that science or scientists promulgate, but there is no experiment to show that there's no soul, or that magic doesn't exist, or that we're not all fundamentally connected, etc.

The underpinnings of the scientific view of the world are what we think of as the laws of physics or the laws of nature. Physcial laws, inferred from physical observation and experimentation and modeling, carve out specific relationships between cause and effect within the physical universe, but they don't show or imply that those relationships are all that exist. They're limited to what's observable by scientific instruments and is within the realm of testability and theorization. This means they're limited in a few ways, such as a) to very simple relationships between cause and effect, b) to proximity in time and space (usually) between causes and effects (with some exceptions for exceedingly simple and obvious relationships, such as the effects of gravity), c) to predictability based on physical control rather than psychological principles, d) to causes and effects that can be definitively, quantitatively measured, etc.

Because of the immense efficacy of science in predicting and controlling the world, people eventually assumed that nature must be wholly mechanistic. But without being able to predict or control absolutely everything that happens, there's no reason to assume this.

You could say that the laws of physics leave no room for any other type of influence on events, but I'd say this is false. As I've said, the domains and contexts in which we surmise and verify physical theories are limited. Then there's quantum mechanics to think about with its inherent unpredictability, which is where the mechanistic worldview of science bumps up against the open-endedness inherent in reality. If spirituality really means much, it should have some kind of influence in some way on our physical lives, and quantum "randomness" is probably an avenue for that influence.

It may sound like attributing spiritual influence on physical reality to the unpredictability inherent in quantum mechanics is a "god of the gaps" theory, but you have to remember that the idea that the world is made entirely of mechanical, non-living stuff was gratuitous in the first place. There never was a time when science predicted everything, it just assumed everything was inherently predictable and hence mechanistic and lifeless as an extrapolation from the limited scope of phenomena it *was* able to predict and control. When quantum physics came around this inertia scientific thinking had gained lingered, and hence people assumed that either a) the randomness just arises from mechanisms-per-se that we don't understand yet, or b) the randomness is "absolutely random" and meaningless. But instead it should have caused us to retract a little the entirely mechanistic and lifeless view of reality we've developed in the first place.

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I just realized it's not entirely true that I have no conflict, there's one specific area of science in which I do, which I was reminded of in a discussion we're having in #philosophical about instinct:

<JohnGuru> well, the one thing I'm certian of is that brains have fundamental functions too, just like calculators and computers. Any *programmable* structure, any structure that can learn, already has a complex layer of built-in actions that serve as the medium programming or learning uses
<inhahe_> JohnGuru: the really intriguing thing is how many functions that we think are just 'us' or basic properties of consciousness are shown to be attributed to very specific regions of the brain by experiment
<JohnGuru> inhahe, yes, well, I don't find that too surprising.
<inhahe_> JohnGuru: it gives me a little bit of conflict regarding my belief in spirits and intelligence independent of brain, life after death, etc.

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I can think of ways it could make sense, of course, but it's still a little bit nagging.