The Church-Turing thesis only states that the lambda calculus and Turing machines can compute the same functions. It has nothing to do with materialism or dualism and it certainly doesn’t state that the universe is a Turing machine.
"Every effectively calculable function is a computable function" [1]
The definition is a little terse so we have to expand on what "effectively calculable function" and "computable function" mean.
By a "computable function", we mean a Turing machine. The term "effectively calculable function" is a little unclear but one definition that I think is the closest to the intent is "it can be done by a human without any aids except writing materials." [2].
In other words, the Church-Turing thesis is saying:
"All physically computable functions are Turing computable"
That is, the physical world, including human cognition, can be realized by a Turing machine.
While one formulation might be cast in terms of lambda calculus, this is hiding the underlying assumption that lambda calculus is used as a proxy to simulation of the physical world and, as a subset, human cognition, effectively saying "if it can do lambda calculus, it can do the physical universe and can do human cognition".
[1] https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis#S...
[2] https://en.wikipedia.org/wiki/Effective_method#Definition
How did you get to the conclusion that all physical world is computable? Rather a huge jump i would say. Sure some things are, but "all of it" would rather be a BIG assumption. Physical theories of the world are limited to our current state of observations and knowledge of the world, they AREN'T the actual world. Who is to say this continuous search, observation and refinement of theories will ever end and we'll have a FINAL theory of everything that we can then plug into a computer and simulate?
Sure you can now say "I don't require a theory of everything, I just need a "sufficient" amount of theory to simulate the part of the world from which I can have my intelligence & cognition emerge". Sure you can say that but that would again hinge on the assumption that such cognition is reducable to these "sufficient" laws.
Likewise saying that the whole physical world can be realized by a Turung machine is a bit rich when we don't even know if such a complete reduction of the physical world is possible and when such reduction to physical laws is surely not yet complete.
EDIT: grammar
That’s not the conclusion, that’s the whole thesis. The whole point of it is that yes, it’s not provable, but so far we haven’t seen anything to suggest the contrary. All of our current physical theories are very much computable, for example.
And we know that we can define an infinite amount of problems that can not ever be computed (or else you can for example solve the halting problem). So there would be infinite amount of questions about the world that we can not ever answer.
And there would be more questions that we can not answer (they are uncountable) than we can answer (they are countable). So if you have a question - chances are such that it can never be answered.
edit: more likely never can be answered.
Like I said all current theories are based on current state of observations. Who is to say we don't observe something in the future for which these laws need to be revised? Who is to say this doesn't keep happening indefinitely? If such a "bottoming out" cannot even be conceived of, saying that the physical world, even a part of it, is exactly computable AS IT IS (all aspects of it) is utmost arrogance.
What do we know about the brain? how does it generate cognition? why does the color 'red' look like the way it does to you; does it look like the same to me? Unless the nature of such cognition and such a being which embodies this cognition is known one cannot say it is reducible or "emergent" from the CURRENT set or even any FUTURE set of physical laws we know or will know about.
The map is not the territory however minute in detail it becomes. Sure this map can become the territory itself by becoming it but then we cease to call it a "map". Say you want to understand how pendulums work, you make a pendulum, play with it. No one's going to call this actual pendulum a "simulation".
Also our physical theories are only computable with an arbitrary halt thrown in at some level of accuracy deemed good enough. And there too theoretically questionable trickery like renormalization is used to reduce the problem to a tractable size.
In the case of transistors that is because all that matters are binary stable states, which reliably abstract over the complicated device physics. In the case of biological cells and neurons in the brain it is much less obvious what the reliable abstraction is. Right now a lot points towards "it is just a bunch of linear algebra and lots of data", but especially when we come to things like memory, online and few shot learning, the answer becomes far less obvious.
In other words, God has been a replaced with a very small shell script.
So, even if an intelligent creator is ultimately responsible for our plane of existence, there may not be much in the way of intent or even observation associated with that responsibility at any scale we would find meaningful.
Heck, who is to say that our particular simulated universe isn't just a honeypot of some sort?