I have spent many years studying both Theology and Philosophy and am currently finishing my MA in Systematic and Philosophical theology from the University of Nottingham. Your observation about axioms is spot on. Wittgenstein described many religious arguments as playing word games. Two individuals can argue all day long, but if their definition of a term is not the same or at the very least agreeable, then there is no definite conclusion to be had.

American evangelicalism has one of the weakest systematic theologies and is built primarily upon fideism. One must give up outside thinking and enter the circle of cohesive thought to know anything at all. This goes against historical Christianity which in fact relies on eyewitness account and outside data for its conclusions. It is also common for evangelicals to assume things about Christian doctrine that Scripture does not necessarily reveal. Animals and souls for instance. The Imagio Dei does not inherently imply that animals are without souls. And in fact, if one believes in the fall, he believes that man has rejected the Imagio Dei.

The problem is not necessarily religion or Christianity but is the circular reasoning and fideism adopted by American Evangelicalism.