People are disturbed, not by things, but by the principles and notions which they form concerning things. Death, for instance, is not terrible, else it would have appeared so to Socrates. But the terror consists in our notion of death that it is terrible. When therefore we are hindered, or disturbed, or grieved, let us never attribute it to others, but to ourselves; that is, to our own principles... -Enchiridion Ch 5
Stoics view mortality as a natural and fundamental aspect of life. We exist in an ever-changing universe. Therefore, much of stoic practice is meant to instill a consistent recognition of the impermanence of every aspect of life. Now, if you live in a culture that hides death away, be prepared for the backlash. As more Stoics become vocal about our philosophy, there will definitely be criticism concerning our views. And let's face it, the concept of death tends to strike at nerves.
Caitlin Doughty, mortician and talented blogger, posted about her experiences with criticism in Death is for Everyone (a bit of a rant, really) . She is not a stoic, to my knowledge, but she is at the forefront of a movement to bring death back into our lived experience. As she reminds us, "Death is not a fad. Talking about mortality is not a trend piece like artisanal pickles or hand-carved charcuterie boards. It’s not something that “hipsters” are doing now. It is the fundamental core of the human experience." I enjoyed her post, and recommend it to you.
And just in case you hadn't stumbled across Stoicism's position on death yet, here's one more quote.
Let death and exile, and all other things which appear terrible be daily before your eyes, but chiefly death, and you will never entertain any abject thought, nor too eagerly covet anything. -Echiridion Ch 21
I'm going to say that if a stoic teacher is advising daily visualizations concerning death, you have to view mortality as pretty central to the Stoic mindset. Now, Epictetus is not instructing us to be morose. On the contrary, death only "appears terrible." The goal is a daily recognition that death is neither terrible nor good, it is simply a fact. That fact, however, is a powerful one and can shape our decisions concerning what truly matters in this mortal life.
So as we go around accepting Death, remember that we are the healthy ones. Living in accord with the world's terms is wise. So go forth, be mortal, and memento mori!