The debate over the relationship between science and religion appears to generate an abundance of 2-by-2 matrices.
Robert P Crease provides an interesting example in Physics World, where he classifies the different approaches to the debate according to whether science and religion are treated as methodologies ('processes') or fixed sets of beliefs.
Crease himself subscribes to the bottom-right quadrant, arguing that "Humans...inherit imperfect patterns of behaviour, and a religious life is the response to the feeling that we can 'live better' than we do." This betrays the familiar religious ploy of attempting to conflate religious beliefs with moral and ethical beliefs. If the sole basis for Crease's adherence to religion is a feeling that we can live better than we do, then what he actually subscribes to is not science and religion, but science and ethics.
The conflict between science and religion is primarily a conflict between science and theistic religion, where "theism is the belief that there is an all-powerful, all-knowing perfectly good immaterial person who has created the world, has created human beings 'in his own image,' and to whom we owe worship, obedience and allegiance." There is no sense in which theistic religions can be treated as just a way of living.
Sean Carroll meanwhile, defines a 'grid of disputation', and argues that atheistic scientific advocates should engage only with worthy opponents, rather than the crackpots (such as the creationist lobby in the US).
Carroll begs to differ, however, with Richard Dawkins, on the question of the best way to change people's minds. Dawkins argues: "I think we should probably abandon the irremediably religious precisely because that is what they are – irremediable. I am more interested in the fence-sitters who haven’t really considered the question very long or very carefully. And I think that they are likely to be swayed by a display of naked contempt."
As Carroll astutely points out, whether or not people choose to use ridicule or reasoned argument seems to depend, not upon any empirical evidence for which is the most effective technique, but upon "the mode to which they are personally temperamentally suited."