Your premise is false, therefore, accounts in media of evil should have no effect on a Godly man.
I question the premise that imagination of evil encourages us to do real evil. For instance, in Puritan times, preachers encouraged the congregants to imagine evil in order to scare them. But there's no evidence that the Puritans did any more evil than anyone else -- and probably less.
That said, the obvious reaction to news of monstrous evil is to ignore it and imagine pure goodness.
How about instead of being influenced by evil, you combat it.
Think of all the charities, all the societies, all the non profit organizations that are instituted to combat evil and harm.
Educate people in the ways to prevent evil, turn a blind eye to the influences of it.
(ex. Mother Teresa)
- I am not a godly man, but I am still a man that believes in right and wrong.
Evil IS, it is not imagined, just as GOOD is. These have nothing to do with whether one believes in a "God" or not. When a person deliberately seeks to do harm to others that is "evil". As I have told kids for the 100+ years I have been teaching, there is enough accidental pain in the world, one does not need to deliberately set out to inflict pain on others... "I didn't mean to" is reponded to with, "then mean NOT to".