Death is something that none of us can avoid and that catches up to everyone at some point or another. Because of this lack of control about when and how it will happen a lot of people tend to fear death above all other things. In fact fearing death is a survival instinct that is built into every living creature on the earth.
An insect struggles to escape from a spiders web not because it is eager to get back to its work, but because it instinctively doesn’t want to die. This is the basis of all conflict in nature, one thing killing another for food, and the prey fighting against this happening. Similarly larger animals such as a gazelle being chased by a lion will try everything it can to avoid being caught and eaten.
Obviously from an evolutionary standpoint this is because of the need to pass on its genetic material and continue the population into the next generation. because of evolution and survival of the fittest, many different species have even developed various methods of avoiding situations which may lead to their deaths. For example animals such as zebras which have camouflage against predators. Or animals such as tree frogs that produce toxins so that no other animals can eat them.
In humans fear of death could well be the starting point for all of our other fears as well. The things people fear are as varied as they can be. From deadly things that are best avoided at all costs, to benign objects or animals who can do us no harm whatsoever. These all tend to be fear of some kind of harm from the thing that we fear, meaning that all things that humans fear are in some form or another an indirect fear of our own mortality.
Because of this it seems likely that to some extent we all fear death on some level. Even if we do not fear death itself as an immediate threat we might be scared of for example lightning, or tarantulas. Both of which have the capacity to kill us. The fear of death in itself tends to come at older ages when death is a lot closer. It only tends to be then that we really think about death and the ramifications of what that entails.
Some people believe in religion largely because of the fact that in most religions death of the body is not the final ending for a person. Either their spirit or soul lives on, or they are reincarnated. This again is proof that a lot of people really do fear death, even if only subconsciously, which guides their actions.
This explains why some people find comfort in religion when they are facing death because of things like old age or terminal illness. When they had absolutely no interest or belief beforehand. Whether they truly believe of not in a lot of cases this is likely to be because of an innate and inbuilt fear of death than no one can avoid indefinitely.
Humans, because of intelligence and reasoning powers, have to some degree managed to pull away from their instincts purely guiding their actions of course. But as much as some people may think they have control over their fears, instincts mean people will always fear death to some extent.