The man that is discussing perjury in Act II of George Bernard Shaw's Mrs. Warren's Profession is Reverend Samuel Gardner.
Gardner is described verbatim as:
"...a beneficed clergyman of the Established Church[..] over 50. He is a pretentious, booming, noisy person, hopelessly asserting himself as a father and a clergyman without being able to command respect in either capacity.
This description contradicts what he is expected of as a clergyman: He is a man of the cloth, which means that he has a a lot of responsibilities towards his followers. However, his character is very flawed; he is ambitious and we can tell his reality as early as Act I when we find out that he is not at all pious, and that he has a very dark past that includes Mrs. Warren, blackmail, and other bad behaviors. He is a drunkard and he is a static character, meaning that he does not change his bad ways at all throughout the play no matter how the plot may or may not affect him.
However, in Act II, when he talks about perjury
The perjury at the Winchester assizes is deplorable.
He is just showing a facade of righteousness and prudishness that is typical to GB Shaw's writing style; one which directly points at the hypocrisies of society, particularly of those who are titled and thought of as "respectable" without questioning their actual behaviors.
Therefore, Shaw gives us a hypocritical "man of God" who acts more like a man of his own liberties. Therefore, that he is passing judgement over the bad actions of others is ironic and ridiculous at that coming from him.