> As an example, you seem to be complaining that their Monte Carlo code has non-deterministic output when that is the entire point of Monte Carlo methods and doesn't change their result.

Not so fast. Monte Carlo code turns arbitrary RNG seeds into outputs. That process can, and arguably should be, deterministic.

To do your study, you feed your Monte Carlo code 'random enough' seeds. Coming up with the seeds does not need to be deterministic. But once the seeds are fixed, the rest can be deterministic. Your paper should probably also publish the seeds used, so that people can reproduce everything. (And so they can check whether your seeds are carefully chosen, or really produce typical outcomes.)