What are some examples of traditional beliefs and their scientific explanations?

One belief is life after death. People who "die" and then come back to life report going through tunnels, seeing bright lights, seeing dead relatives, and maybe even seeing Jesus. (I always wonder what they say Jesus looked like, was he the English version of a light-skinned, blue-eyed man with dark brown hair, or was he the dark-skinned, dark-haired Jew described in the Bible?) Science now knows that these "deaths, visions and hallucinations are caused by the release of DMT into the brain. This powerful *** that is responsible for these experiences is reported.

What are the similarities between the process of obtaining religious and scientific explanations?

Stephen Jay Gould's observations about science and religion are very relevant. His statement that there are "two non-overlapping authorities" says all that needs to be said. There is no "similarity" because the two magi are completely different in their most basic nature.

It is the eternal mission of religion to preserve, protect, and disseminate (allegedly) a specific set of ideas derived from supernatural sources by individuals with recognized agendas, preconceived ideas, and prejudices, and promoted by authoritarian institutions. Changing the basic precepts is to be avoided at all costs.

Science, on the other hand, never starts with a preconceived idea and then carefully selects data to support that idea. Instead, science begins with a hypothesis - a statement about reality that is then tested by trained practitioners through the most rigorous procedures, and then discussed, questioned, and validated by numerous outside practitioners until it gains widespread acceptance based on its ability to explain current phenomena and accurately predict future events.

The two strategies for obtaining "explanations" are diametrically opposed and mutually exclusive.