Sure, axioms are the basis of our abstract thinking. But simply beeing aware of that basis allows you to change your perspective/abstraction towards stuff.

You dont have just one body of beliefs, you try to have a qualified take on all of them. This is where your question revolves around. Whats "a body of beliefs"? And is it open or closed?

Its the difference between aproaching realitiy heuristically (and never reaching a final answer, thus constantly revising your thinking) and just picking one set of beliefs/axioms/ideology and call it holistic, like religion does.

Its the way of the sceptic and imho the only way we should think ... or at least be aware of the heuristic nature of thinking.