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Axiom 1: An external objective reality common to all exists.
This is pretty much the definition of Realism. At the opposite end of the spectrum is the Idealism of Berkeley, and somewhere in-between the two is Instrumentalism.
Regarding the original question, does it matter which school of thought you subscribe to when it comes to assigning validity to the empirical investigations of science? Basically, no.
I think the biggest misunderstanding held by most laymen, and even many scientists, is that science is a school of thought or an attempt to establish absolute truths. Science is simply a method of inquiry into the world available to the senses. In this method, the observer is of prime importance and the scientific test for 'validity' is nothing more than direct or indirect observations. If it looks like a duck, acts like a duck, then by definition it's a duck, even if a theory states it should be a cow or a horse.
If I state I am holding in my hand something that is round and red and ask you to discover what it is, you will conduct an inquiry using a particular method. The object could be a ball, an apple, or I could be hallucinating or simply insane. What matters most is not the answer but the method used to go about answering the question and the criteria one chooses as a standard to verify the result.
In your effort to identify the object, you would likely ask many questions -- Is it organic? What's the weight? How big is it , etc...One thing you would most surely not ask is, "Is the object real or are you hallucinating?" To conduct the investigation, you don't need to know that, even if I was hallucinating. The assumption is the object is real and the goal is simply to use the method to achieve an end.
In the case of the scientific method, the only way one could verify and validate the conclusion would be a direct or indirect measurement or observation that would then be compared to measurements and observations already made in the past.
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