How does one make a race that worships a personification of Death less evil? This race believes that dead souls go back to the River of Life to be reincarnated into a new form, so their beliefs aren't particularly radical or extreme. However, I am afraid that their death-worship may still rub people the wrong way.
It depends on how they worship, not what
How do they Worshipp death? Do they go all “Kool-aid rapture”, or is it simply honoring those who have passed. As long as they don’t sacrifice humans (or at least, innocent people) they will not seem evil at all.
Have them celebrate death rather than being all macabre about it - think Mexican Day of the Dead style.
Then assure that they aren't trying to shuffle people loose the mortal coil a little early.
Death is a necessary part of life.
Depending on exactly what you mean by "race", this could be about a subgroup of humanity or it could be about a completely alien species. Either way, it's difficult to live if there is not death; if nothing else, an unconstrained population will sooner or later overshoot the ability of its biosphere to support it, causing famine, illness and death. An immortal species even more so, if they procreate at all. Some kind of death is necessary to keep their own population in check, and some kind of death is likely necessary (one could make a philosophical argument that harvesting plants is not the same thing as killing, hence likely) for the continued survival of the race.
Recognizing this, your race views death not as something evil, but as something ultimately necessary and possibly even honorable.
It then becomes a sacred duty of sorts for individuals to eventually die, and those who remain alive remember the sacrifices made by others that allow the continued survival of everyone else.
This isn't at odds with killing others of one's own kind being thought of as wrong; knowingly taking the life of another need not be the same thing as accepting one's own, or another's, eventual death. If your race is one of carnivores, they may even distinguish between killing for food, killing in self-defense, killing in defense of others, mercy killing (say, a member of the group being mortally wounded during a hunt being put out of their misery) and killing for other reasons, which itself could give rise to interesting moral conflicts.
Whichever way you go, something like this is going to show through in various aspects of society, not least of which in rituals centered around death and the deceased.
Death is not evil. Death is a process. It is the act of violence or murder that is considered evil. Consider these points:
Natural death is considered an inevitable end. Their time is done and they must return to the maker by his side or in your case to start a new. Anyone who lives longer then they are suppose to (e.x. immortal) is considered unnatural. Make up a legend or a story that would explain that.
Murder is a taboo. Taking someone's life is considered bad even if they worship death. No human sacrifices, or if you have to try to make it do not use knives or spill blood. It would be nice, if the tribe believe so, to point out that killing they are against.
Set rules of what they considered good and bad. Embed them in their actions or tales, so it feels more natural when you present it to the person.
Consider an idol or a statue of Death. Make it a woman with flesh rather than a skeleton with a scythe if you can. After all that image of the reaper was created to scare people.
Also calling it "The River of Life" instead "of death" has already made them not sound so evil.
A lot of good answers so far, but just wanted to add.
Its the opinion of others that count as to how a religion is viewed, if you are a member of that religion then it would seem normal to you, however a "non-believer" is the one you need to convince that its a normal religion. It's also often what that race does in general that defines that viewpoint on the religion itself, specifically historically in the real life
Christianity is seen as a happy and peaceful religion, but i'm sure in the days of the Crusades this was not entirely the case, but after a few centuries and with the vast majority of Europe being part of that same religion, the opinion became what we know today of it being good (yes this is an oversimplification)
Islam is, at its core, a religion dedicated to peace, unfortunately a very small minority have used it to spread terror, and thus is widely looked upon as bad.
Going further back the Mayans and Aztecs aren't really looked upon badly for their religion, yes not vast amounts survived like they did for Egyptian/Christian/Jewish/Islam but people see what the Mayans did with astronomy and both did with construction etc, and look somewhat fondly on them, despite human sacrifice being common during religious services.
So long as your culture that belongs to this religion is peaceful then often outside people will think of it as peaceful no matter what it is they believe. and to be fair, you've already explained it in a way that makes it sound peaceful or at least not very macabre.
They hold death so valuable that they go great lengths in preventing anybody from getting undeserved death. And they're good at it since they know so much about death.
If you have a ride-along character, have them receive an explanation from one of the faithful.
As weird as it may sound, try avoiding the word death. Place more emphasis on the aspect of being “reborn” or “ascending.”
Also, consider how the deity looks and behaves. Have depictions of them appear in bright colors. Describe them as physically beautiful and not monstrous. Have they moment they come to claim the faithful described as a warm embrace.
Finally, show their culture and social structure in a positive light. Show that they revere death by natural causes, not by inflicting it.
I hope these ideas help.
Make your Death character sympathetic, and make the worship focus on that sympathy.
They can have texts where they appreciate the difficulty of the job she has, and acknowledging the love she shows when she eases people of their suffering and guides them to the next life. Maybe a story where there's a family weeping over a sick child, and when Death comes to take the child she weeps as well, and cradles the child gently into the River of Life; later those tears turn to tears of joy when she recognises the same child, born to a new life where he grows to a happy adulthood.
Comforting the bereaved: they believe that death is natural, inevitable and desirable, but still acknowledge that it is sad and frightening at a personal level. They take great care to ease the pain of people near death, and have rituals allowing family and friends to say goodbye.
Death must not be trivialised: they believe that Death's duties are important, but that Death as an entity is not all-powerful. If many people were to die at the same time, that may overwhelm Death and lead to the River of Life being polluted by poorly-treated souls. Therefore they avoid war except as a last resort, never execute prisoners of war, and practice the best medicine available.
Sustainability: the River of Life continues forever, so they must ensure that the world is always ready to receive the reincarnated souls. They do their best to protect the environment, do not waste resources, and keep a detailed record of history in the hope that souls may find the world familiar from their previous life.