Keep in mind the specific group that we are talking about in this post. The American Evangelical conservative. They compose a subsection of the larger group of 'Religious people.'

This group openly and unabashedly pursues and promotes science denying, literalist interpretations of the bible that run counter to what we can think of as scientific consensus. Young Earth creationism is one example. The teaching of abstinence-only sex education as a method to reduce incidence of teenage pregnancy is another. The point is that this group is very good at saying 2 + 2 does not equal 4. When you have practice in this you are better at it than people who do not.

The American Evangelical conservative composes some percentage of all religious people. The American Evangelical conservative is better at Double think than the average person. Religious people when taken as a group can be said to be better at doublethink because constituents of the group are.

To use an example of specifically twisting words:

When a parent abuses a homosexual child when they come out or afterward, many will say that they love their child and that the abuse is motivated out of love. To the best of my knowledge one cannot love a person and also physically abuse them. The word has been twisted. I don't know of many non-religious people who abused their children when they came out of the closet. If this example is particularly vulgar or hateful I'm sorry but it is the first one that comes to mind because it is close to my heart.