IPA: /ˌɪrɪˈlɪdʒəsli/
KK: /ɪrɪˈlɪdʒəsli/
In a way that shows a lack of religious belief or respect for religion.
He lived irreligiously, often questioning the traditions of his upbringing.
Irreligiously → It is formed from "ir-" (meaning not) and "religious" (from Latin "religiosus", meaning devoted or pious) and the suffix "-ly" (meaning in a manner of). The word "irreligiously" means in a manner that is not devoted or pious, often implying a lack of religious observance or respect.
Think of 'not' ('ir-') being combined with 'devoted' ('religious') to remember that 'irreligiously' means acting in a way that lacks devotion or respect for religion.