Both of these plays show an extreme form of cruelty and corruption, some of which is due to religious hypocrisy, and some of which is due merely to human nature in its worst guise.
In The Jew of Malta, we see the typical (for European societies at the time) discrimination and hatred directed against a Jewish person. As soon as the Maltese leaders learn that the Turks are requiring tribute from them, their first thought is to demand (i.e., steal) Barabas's money and use this for the tribute. This is rationalized entirely by the fact of Barabas being of a different religion—of his not being a Christian—though it is a direct contradiction of Jesus's injunctions about wealth and about how people should be treated. The governor, Ferneze, makes no secret of the reason for targeting Barabas, as he tells him,
through our sufference of your hateful lives,
Who stand accursed in the sight of heaven,
These taxes and afflictions are befallen.
Though Barabas's subsequent actions are in response to the cruelty enacted upon him, he is a hypocrite as well, poisoning the residents of a convent and then planning to murder the Turkish leader Calymath by hiding barrels of gunpowder and blowing up the hall where he and his men are meeting (in a plot which seems to anticipate the real-life plan of Guy Fawkes to blow up Parliament a little over a decade later).
In The White Devil, the direct focus on religious hypocrisy specifically is even stronger. The characters are supposed to be devout Christians, of course, but they're all at each other's throats. Brachiano and his secretary, Flamineo, devise the murder of Brachiano's wife, Isabella, and Flamineo's brother-in-law because Brachiano wants Flamineo's sister Vittoria. When Vittoria is subsequently put on trial, the Cardinal (and future Pope) Monticelso hurls a stream of abusive language at her, calling her a "whore," a "creature," and so on. We also learn that Monticelso has kept a little book containing a list of names of people he can blackmail. Altogether, it's a criminal atmosphere, in which both the nobles and clergy conspire together to achieve sordid aims.