[quote=Lo Pellegrino]they deserve to be taken seriously[/quote]

This is exactly what I'm getting at.

Now, I do have sympathies for your situation. Those people are assholes, your skin colour has nothing to do with your ability or right to sell a product at a certain store.
But taking it seriously is just that, taking it seriously. You are giving acknowledge and credit to it, which in the eyes of the one making the said threat only further validates the threats and let's them them they may actually have the power to do it (even if they in all likelihood wouldn't regardless).

I mean, if there are past actions to indicate they are actually able and willing to do said acts?
Such as say the guy giving the threat just got into a bloody fight, the guy threatening people of colour has actually closed places with people of colour or fired coloured employees?
Then that adds legitimate concern and worry, enough that it's not just empty words and you should be trying to act on it.
But the majority of the time it's not that, it's hot air. Hot air that only get's encouraged/reinforced when people take it seriously.

[quote=Touch of Insanity]Also as taking death threats seriously, even if people really don't mean it, my younger sister in high school got into a pickle because of something like this. A group of her and her friends were writing death threat song lyrics that were implying to hurt and kill another student. the student's girlfriend called the cops and at 10:30 at night a cop showed up at our door and told her, even if she didn't mean it how serious it is.[/quote]

Honestly, I think the cops mainly take that stuff seriously because of pressure and diluting.
Pressure as in pressure from concerned/over-protective parents for the Cops to do something and diluting so they can try to sort out fake death threats from the real ones from when a case is underway.

Now, I do want to clarify.
I am not defending death threats in the slightest, they are shitty thing to do and no one should stoop to that level, ever.
But I don't think we're helping the matter by treating every one of them like it's a serious threat/ordeal.

[quote=Touch of Insanity]If you're reported making a threat to someone's life, if anything happens to that said person (can't remember for how long) the cops will always come to you and question you think you hurt them.[/quote]

That's only logical. If the person was actually hurt/harmed, it means someone meant harm. 
So logically the easiest place to look first are those who expressed desire to hurt them, even if the odds are low it's better than nothing.
It's a lead, police follow leads. Plus, they probably don't even think you hurt them most of the time. But they have to keep appearances of that they're certain/positive about what they think, it's a common tactic used by authority figures, parents, teachers, admins/moderators, bosses, you name it.