A bunch of atheiststs debating semantics is about as useful as a bunch of religionists frothing over hermanuetics. Sophistry is sophistry, pedantry is pedantry, with or without a god.
Of relevance here might be Lugwig Wittgenstein's
Tractatus Logico-Philosophicus. The introduction, by
Bertrand Russell, is itself a masterpiece of critical thought.
However, casting prudence aside, I'll wade into the fray with a bit of hermanuetic sophistry of my own, however pedantic that might be. I would posit that to be
irreligious is, in the conventions and within the limitations of the English Language, to be contemptuous, disrespectful, and dismissive of religion. To be
areligious is to be without religion or religious influence. One may not be at once dismissive, contemptuous, and disrespectful of a thing and be at the same time uninfluenced by the occasion of that contempt, disrespect, and dismissiveness, as those attributes clearly are influences on the individual in question.
IRreligiousness may by a stretch be considered a form of Religion, whereas
Areligiousness is by definition a lack of religion, an absence of it and/or its influence.