"stir up hatred" is a correct and usable phrase in written English.
It can be used to express a degree of inciting or provoking animosity or ill will. For example, "The political candidate attempted to stir up hatred in the public by spreading lies about their opponent."
I would make exactly the same point about people who stir up hatred of any other group.
They define hate speech in terms of the manner of speaking (threateningly, abusively) and in terms of its intended object (to stir up hatred against some group).
As food shortages loom, Mr Mugabe seems to think his best hope for retaining the presidency next year is to stir up hatred of Zimbabwe's small white population.
They can't do much to insist that the press doesn't twist or misrepresent the facts, doesn't stir up hatred with relentless falsification.
A leading association of Muslim academics based in Qatar and lead by preacher Yusuf al-Qaradawi claimed it would "stir up hatred".
Some — especially non-Chinese commentators — think they are paid to stir up hatred and resentment of foreign countries such as the United States.
"National Action is a racist, antisemitic and homophobic organisation which stirs up hatred, glorifies violence and promotes a vile ideology, and I will not stand for it.
The hardest lessons of history must be learned again and again: nationalistic fervor is a hollow construct, enough to stir up hatreds, enough to fill malleable minds with false pride and hubris, but in the end, it is not enough to ensure victory.
Just the fact of imagining Muslims taking power, imposing Sharia law, stirs up hatred.
Labour's Jack Dromey said Trump was dangerous because he stirred up hatred among different faiths.
A change.org petition urging Channel 4 to stop broadcasting the documentary on the grounds it promoted a "skewed image" and "stirred up hatred" received 60,000 signatures.
