Socrates often considered the father of modern philosophy clearly thought that the fear of death is irrational much to the bafflement of his friends who offered to rescue him.
Epicurus and his argument for why the fear of death is not rational is based on the idea that once dead we no longer feel pain, pain is bad thus death is not bad. A sound argument the conclusion follows logically from the premises, yet I do not think that it is Death that people are truly afraid of, either there is an afterlife or there isn't ,either way it doesn't really matter, it is dying which people fear. Epicurus makes no allowance for the process of going from life to death which can be quite painful, so by Epicurus theory, bad. So perhaps he should have asserted that death is nothing to us, dying is a different matter. In my opinion this is Epicurus only major shortfall and I agree with most of his assertions about death such as the idea that death is a fitting end for life, we start as nothing, we return to nothing. What was perhaps most unique about Epicurus was his admission of slaves and women into his garden to learn, now a days this may not sound very significant but at the time in ancient Athens when no slaves or women could vote and were considered almost second class the readily acceptance that they were met with ensured that Epicurus teachings lasted.
Although I think it is irrational to fear death I can see why people do, no one knows anything about what happens when we die, people can theorize and ponder as much as they want but it is still an unknown quantity, it is still x. It is partly for this reason that so many people flock to religions and one of the key features of a religion is the belief in a god, and an afterlife and it is partly for this reason that Epicurus strove to eradicate peoples fear of death so they can get back to enjoying their lives and living pleasurably as this is what Epicurean teaching is all about, so yes I think that the fear of death is irrational for the very reason why people fear it we don't know anything about it and if we don't know something how can we fear it and its not like its only us who dies, everything dies the earth too will share our fate eventually.