The same thing can be said about "which model of computation resemble physical reality." Each of us can have different mental models of physical systems. Personally, the functional paradigm is closer to my mental model than declarative, but imperative still feels the most natural. This isn't a statement about reality, but rather about how you think about it.
That being said, of course it matters the way you write your software. There is a huge gap between actual CPU instructions and Lisp. Between Lisp and the machine is an automated, soft layer of emulation, which may or may not be optimal and is extra work anyway.
F=MA is a function, and it isn't mutable. I could calculate force from some other function (e.g. Gm1m2/r^2). I can compose those functions together to get a new function. Still nothing mutable. I could continue this to create a model of a physical system that turns into one big function. That function models the system, and it can take some outputs to give whatever outputs you want. All without storing state internally.
So, it's certainly possible to accurately represent physical systems without keeping track of state along the way.
Classical state of a particle lives in the 2n-dimensional manifold known as phase space. The coordinates of the phase space are the configuration space and the corresponding conjugate momenta. The state is a single point on the phase space, corresponding to the initial conditions of the problem. The Hamiltonian determines the time evolution in the phase space, which is a trajectory.
To make is simpler for you to understand: 1. Position and momentum couples form the physical state. And of course, for any physical system, it exists. 2. You need 2 initial conditions to solve a 2nd order differential equation. You can't solve a differential equation without initial conditions (of course to use this fact, you would need to understand that F=ma is a differential equation, not a function) (Maybe it's better if you read some good introductory text, such as Feynman Lectures on Physics Vol 1, Chapter 9).
If still not clear for you: the initial state in a two body problem is determined by the initial position and velocity. They are the initial conditions of your "function" F=ma, which is actually a second order differential equation. F determines how this initial state will change over time.
CS people like to abstract away the computation from physical hardware, but the apparent fact is computation _is_ physical, and it's limits lie in physics and not in mathematics or philosophy (see Shor's algorithm for instance).
It's only natural to write programs in a language that follows the same flow as the underlying physical computer. A classical computer is represented by it's assembly language, thus it makes sense to have languages like C. Concepts like "stateless programs" don't even exists in a classical computer. It's as crazy as trying to build a quantum algorithm that does away with measurements!
In addition the physical world does not work anything like a stateless machine. As most useful programs imitate a physical process rather than a pure mathematical object, the notion of writing programs in such languages is not-intuitive and requires transformation of the actual problem at a both low (hardware) and high (software output) level.
Finally I would like to speculate that the whole concept will never be intuitive in the future (post-quantum computer era). In the era of quantum computers, because they will always be physical objects with a particular state, and it's this very fact that they have a well-defined state allows us to perform a computation.