The Logical Fallacy of Creating Misgivings / Ad Fidentia occurs when tactics are used to instill irrational doubt or fear into the minds of a group of people. The most common way this is done is through character assassination; however, the tactic can be used against a concept, organization, class of people, or anything else.
"If you teach that the history of the Bible is to be taken literally, you will turn people away from Christ."
"If you teach that sexual sin is wrong, you will turn people away from Christ."