For example, if you consider the problem of evil. It follows rationally, that a god cannot be omnipotent if evil exists. This then leads to that either the theist will ignore the argument and pretend they never heard it. Or they will adapt the compartmentalisation in where they can only consider one aspect of the argument and ignore the other. Then when you bring up the other point they will completely forget everything you just said and start again.
In the same way, an omniscient god cannot be compatible with free will. It is illogical to believe that you have a choice when the decision is already known. So when I ask does free will exist, a theist will say yes. If I then ask how is this compatible with an omniscient god, they will reply but we are not talking about free will we are talking about omniscience.
Compartmentalisation is a great way to sort your ideas, post or music on your hard-drive. However compartmentalisation is not a good way to sort your mind if there is no flow of information between the different compartments. Or to use another computer analogy, would your media player be able to work if it could not share files in your music folder?
This compartmentalisation is what I believe is the only way a theist is able to maintain their beliefs. After all its easy when you can plead ignorance on so many levels. Or to put it in another way, saying "I don't know" if someone is asking you questions on a subject which you are not able to logically process by sharing information between the different compartments.