Meaning : Without respect.
Example :
The student irreverently mimicked the teacher in his presence.
With reverence. In a reverent manner.
He gazed reverently at the handiwork.Meaning : In an irreverent manner.
Example :
In the seventeenth century England had known fifty years of doctrinal quarrels and civil war; clergymen had been turned from their cures, and churches irreverently used.