I believe that double-think is possible and sensible. It generally takes the form of making a deliberate attempt not to learn more about something, and not bothering to assign an expected value to the information you are missing out on.

People avoid watching horror movies if they want to stay composed. They try to avoid internet shock sites if they don't want to be disgusted. In a similar way, avoiding information that contradicts a belief that

1.) would be painful to discard

2.) exists in an area where accuracy isn't terribly important

makes sense. For example, if I am a fan of some football team, it makes sense for me to avoid reading articles critical of that football team.

A corollary is that god-belief of the right sort makes sense for people who aren't scientists, politicians, or philosophers.

Another situation where double-think makes sense is when you're trying to avoid seeing information which will make you regret a decision, or might influence you to change your decision, but with the potential for only marginal improvement. For example, if I am working in such-and-such a profession, it makes sense for me to avoid reading about how a different job is much cooler.