Rationality is defined as choices being able to be made that are both complete (all options under consideration can be understood) and transitive (if I choose A over B, and B over C, then I choose A over C).

Most often people exhibit bounded rationality, as "completeness" is a heavy cognitive burden and transitivity is hard on the margins.

Neither components of rationality require belief, and both recognize that choices (free will) can be made, suggesting more nuance to your argument is needed.