Sentence:  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 <WSD>irreligiosities</WSD> 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. 
Meaning of the word marked with <WSD> tags:  An impious action or utterance.