irreligiosity

The quality of being irreligious.

1584, William Allen, A True, Sincere and Modest Defence of English Catholics, London: The Manresa Press, 1914, Volume 2, Chapter 8, p. 126, And it is a singular note of irreligiosity in our days, that these profane heretics and godless persons do prefer human things before divine; the regiment temporal before spiritual; the body before the soul; earth before heaven; regality before priesthood; and this life before the next and all eternity.

1930, William Malisoff, A Calendar of Doubts and Faiths, New York: G. H. Watt, “The Significance of Science,” pp. 277-278, The irreligiosity of much that passes for religion is paralleled, of course, to quite an extent by the unscientific nature of a great deal that passes for science.

An impious action or utterance.

[…] at first, the sudden insertion of scathing irreligiosities into the mouth of such a previously unflappable character seems a merely academic gesture.

Majlesi preached and popularized his discourse with the open support of the Shah. In exchange, he turned a blind eye to the personal and private impieties and irreligiosities of the Shah, as long as the Shah continued to officially pay lip service to Shi‘ism and publicly act as its protector and upholder.