As a conversational note… there is no “rational” form of conversation between believer and non-believer (or for that matter between believer and believer). The word “rational” alone does not sufficiently describe nor set proper parameters for conversations. “Rational” is a very broad term. I would recommend the American philosopher, Alastair MacIntyre (Whose Justice, Which Rationality?) for those who still hold the mistaken opinion that rationality has any universality in its meaning.
The arguments are interminable and without resolution – for all of the assumptions flow from different places.
As an Orthodox Christian, I would say (in Orthodox terms), that the heart is everything (“heart” as understood in a traditional Orthodox manner). For “out of the abundance of the heart does a man speak.” Thus, what someone offers in their arguments (regardless of rationality), is evidence of the state of their heart and nothing more. And the state of the heart is everything.
The Elder Paisios says that even the “sight of a fox” can be an occasion for conversion. Thus with patience we speak to a non-believer, to the heterodox believer, and even to other Orthodox believers, knowing that the heart is the object of our conversation and not the red herrings presented by various so-called rationalities, be they unbelieving, heterodox, or Orthodox. The heart is everything.