Jakoby is an Orc, and is paying for the mistakes his ancestors made, the Centaur is treated 'fairly' in comparison.
There is unfortunately not much back story elaborated in Bright1. As such, all we know about the past is that:
There was a powerful magical being known as 'The Dark Lord'
The Orcs sided with this Dark Lord
The Dark Lord was apparently defeated by Elves and a band of merry creatures (The Shield of Light), united under the Orc known as Jirak
Orcs never lived down their choice to side with the Dark Lord
Here is what Ward's fellow officers have to say about this:
You know what they say about clan
Once for the Dark Lord, always for
the Dark Lord.
How can dumb-asses like you who
can’t remember your wife's birthday
still have beef against a whole
race of people for some shit that
went down thousands of years ago?
"Race of people."
Bright, Shooting Script, 2016-02-29, Landis, M. and Ayer, D.
Jakoby even makes a meta remark about this when they encounter the homeless crazy dude:
The homeless man points his sword directly at Jakoby...
HOMELESS MAN (CONT’D)
Two thousand years ago we fought
him with swords and arrows! Now he
rises again. We will fight him
with bullets and bombs!
Why’re Orcs always the bad guys?
Note how Rodriguez' response is so poignant
Don’t look at me, man. Mexicans
still get shit for the Alamo.
Basically, things are the way they are, and no one really remembers why. People are just racist.
Conversely to this, there is no mention of Centaurs or any discrimination against them.
1. It is my opinion that David Ayer should have gotten someone who knows how to write fantasy to help him. My tip would have been George R. R. Martin (since he's not busy at all these day).