I would caution you that you are treating the word 'axiom' and 'assumption' as equivalent terms. I do not see them as such.
If what we know is derived from what we experience, and that knowledge is held with degrees of confidence based on consistent corroboration through experience, then I would respectfully disagree that science holds as axioms the conclusions that the observed world is real and that observation provides accurate information. I would argue that science holds these conclusions with a high degree of confidence based on millennia of corroborated observation by billions of observers. The conclusions are not assumed true, taken on faith, nor the propositions of an abstract analytic system. It is simply what we observe. If observations begin to contradict these conclusion, then confidence would be challenged and a reanalysis would be required.
Proof of anything requires command of all the facts. Absent complete omniscience, all that is left to us is the formation of conclusions held with varying degrees of confidence.
In context, I was actually referring specifically to the question of a scientific morality to keep it simple. As noted though, it is also true in general.
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
Basic assumptions of science - Understanding Science