The religious concept of a ‘soul’, the atomic spark of personhood (‘atomic’ in the sense of being a single whole, not composed of parts), is incoherent in most secular/scientist descriptions of the world. In those paradigms, the mind is not atomic, but a composition of parts that bear some relationship to the distinguishable lobes and hemispheres of the brain, which are further composted of their constituent neurons and the connections between them. Changes to the brain can change a person arbitrarily, leaving no room for the ghostly spirit the soul traditionally describes.
But the concept of a soul is still intuitive: we tend to think of ourselves and others as constant in the way that a soul is constant. When a relative suffers a brain injury that changes their behavior, it’s awkward to talk of the event in terms of the death of one person and their replacement by another. Rather, we intuitively see a continuity of ‘soul’. Even a person reduced to a vegetative state, so that nothing of the personality that defined our intuitive understanding of their soul remains, is treated as a continuation of the same ‘soul’.
There are limits, though. If a brain tumor changes a person’s behavior, we may not assign the full legal or moral consequences of their actions to the person. Similarly, we sometimes excuse certain misdeeds done under the influence of alcohol or drugs. And we sometimes allow those in vegetative states to die, when we are confident that the state is permanent.
The limits are also seen at the beginning of life. A newborn is typically considered a moral patient to the same degree as an adult, but a fetus is not. Some religious people think the atomic soul attaches at fertilization, others that it attaches on a child’s first breath. A secular person will tend towards the latter. In a materialist sense, a child’s brain is not very much like an adult’s neither in structure or content, and personhood does not begin to emerge for some time after birth. But the intuitive soul seems clearly there from birth.
These paradigms are hard to keep straight, but they have significant consequences. The animal rights movement, parts of which place significant weight on e.g. the lives of shrimp, are invoking the intuition of soul. Even vanilla utilitarianism quietly assumes a ‘soul’, because utility must be experienced by someone – by intuitive souls. That is not a dig against these moral systems, but in my experience their advocates reject that framing, though without a better explanation of what exactly replaces the intuitive soul.
It seems the concept of a soul is hard-wired in humans, which both makes sense for how it helps us to navigate social interactions, and suggests that secularism/scientism would do well to make peace with the idea. These traditions do a reasonable job of rejecting religious understandings of soul insofar as they reject dualism, but they do less well at explaining how to employ the intuitive concept of soul that remains.