People stereotype because it's efficient. It saves the bother of assessing justice in a more practical and sane way.
Think about it. Poor people get taken into the woods and shot all the time in the USA. Sooner or later the word got out that this country was never all that safe a place to live and that it's getting worse by the minute (not enough Marines ~ my guess).
So, in order to continue to be lazy (and lacking the good sense to join the Marines) bigots tend to want an easy way of determining friend from foe.
It's not merely cowardice, it's also extreme laziness that drives bigotry.
I once had a medical condition that changed, temporarily, my skin color. I'd gotten a bit of snow burn (or frost bite if you will) over about 100% of my body.
I was trying to save some people after a plane crash... but that's too long a story... got into it with some outlaws hiding in the woods on the hike to civilization and was shot and passed out in the snow for awhile...
Anyway, when I got back to civilization after saving the day I was shot by bigots for speaking to a white woman.
You see, I was taken to the hospital white, turned blue-black and was assumed to be a "changeling" ~ a person was assumd stolen from the hospital and I was assumd left in his place. No way the hero turns black.
So, they "placed me ith a black family".
And they went for a visit down south.
Literally, I was fish out of water.
I even talked "like a darn yankee $%&@#".
It's not only that they felt they were in a "fight" with militant people of color and were terrified. They were also far too lazy to even find out anything about me.
The black fellows were nice; "my own" tossed me gunshot into the river.
After I "turned white" again, I was placed with first an Irish family (the IRA shot him for accepting an English child after researching and finding out apparently who I was...)
Then I was placed with a German family. Bit by a spider and nearly dieing they blamed the "cruelty of that race" and gave me to some other family... etc.
Bottom line: people are ideally placed with close relatives.
Cause trauma is trauma.
And for pacement purposes, stereotyping is often better than cleaning up the bloody mess after...
But ~ get competant people into office.
Cause one home I went to tried to skin me alive and sell me as "rabbit meat". Conserfatives believe all lies told by ALL conserfatives, even peopl running "adoption agencies" on the cheap that keep no records of where they place every child.
Because on ocassion the Manson family is running the adoption agency ~ and eating those they can't place ~ and selling the excess children as rabbits.
(You really gotta know the difference between a rabbit carcass and a human to tell... apparently.)
No, I'm not kidding about any of this.
In fact, I wasn't even then a child.
I was a veteran pilot returned home with such bad wounds I shrank ~ and looked "childish". I was in fact the pilot of that aircraft that crashed in the first part o this answer.