Surveys show that older people are generally happier about everything than middle aged people, and that probably includes being less anxious about death.
Before modern times parents might seem to shrug their shoulders even over the death of their own children because it was such an expected routine event. It was a rare family that was spared from some level of infant or child mortality. These days we expect our children to live, we expect to live to 80 ourselves and we now expect governments to be concerned with safety in the workplace, safe travel, etc., so in a sense we are more anxious about avoiding death than we used to be.
However, most animals have an inbuilt fear of life threatening situations, which leads them to try and escape predators, flee forest fires, avoid the edges of cliffs, etc. Fear of death is an evolutionary advantage for all animals, including us.
Humans, though, should surely only fear death if they believe they are going to hell because of their sins. For those who believe they are going to heaven, death should have no sting. That includes most "sinners" who are usually confident that God will forgive their sins, no matter who bad they were.
Atheists should not fear death either, because for them death is "mere oblivion" (as Shakespeare put it). After death there is no pain, no regrets, no anxiety, no awareness of anything past, present or future.
Perhaps wavering agnostics might fear death because maybe hell does exist and they haven't prayed for forgiveness or believed in God. Also, those gullible people who believe in ghosts might fear death as a possible transition to becoming an unhappy, restless spirit for all eternity.
I think many people fear the process of dying more than death itself. It can be painful, and knowing that death is near can be a time for regrets and sadness. On the other hand, many people die peacefully in their sleep at home with no warning, like my grandfather. It was a shock for my grandmother, but she heard him take his last breath and there was no movement, no sign of distress. He simply stopped breathing due to a heart attack. That's the way I'd like to go, and I see no point in worrying about when it will happen, as long as I've made some sensible preparations, such as writing a will.
That's a very thoughtful response, but I don't see things quite the same way.
Certainly, for people who are in chronic pain, or are very incapacitated, death can be a release. Until that happens, though, many people, even sincere believers in an afterlife strive very hard to stay alive. My mother was like that. She was what we call a daily communicant, and was firmly convinced that there was an afterlife where she was convinced she would eventually meet all her departed loved ones.
When she was diagnosed with a primary brain tumor at 61, she did everything she could to stay alive, undergoing two brain surgeries and the implantation of radioactive seeds in the tumor to try to stave off the inevitable. She was very clear about her reasons: she wasn't ready yet. She and my father had just started to travel extensively, there were no more money worries, and most importantly, she had four grandchildren she adored and she wanted to see them grow up more, especially seeing how many people lived into their 80s and had that opportunity. Most importantly, perhaps, she was worried about how my father would handle her passing; she was right about that, as he died barely nine months after her passing. As he said, he wanted to be with her.
However, after the second surgery she was paralyzed along her entire left side and was bedridden. My father, my aunt and I took turns caring for her, but she became more and more depressed. This wasn't a life she wanted to prolong. No matter how much care my father took of her, making sure she never got a bedsore, reading to her, playing her music, cooking her favorite food, it was just too much. Not even he could make her fight it anymore.
So, I don't think belief in an afterlife means you won't or shouldn't fear death.
Likewise, I guess I'm now a sort of agnostic. Even if there is a God, I don't believe in an afterlife. However, the idea of my personality, my memories, my loves, all disappearing into a void is more terrifying even than spending a couple of decades in limbo would ever be.
I've seen "good" deaths where people "are" ready, and have no fear of the afterlife; my grandparents were like that. They were both in their late 80s, getting infirm, even their grandchildren were mostly all married, and they were just tired, I think. My father had a good death too; he was hoping for it because he firmly believed he'd be reunited with my mother, and she was by far the most important person in the world for him, the one person without whom he couldn't contemplate existence.