A motion passed at the NEU's conference in Harrogate described Reform UK as a "racist and far-right party because of its policies around immigration and its campaigns against migrants".
It accused the party of "scapegoating refugees, asylum seekers, Muslims, Jews and others who do not fit their beliefs".
Members agreed that the union should "use the union's political fund to support campaigning against election candidates from Reform UK (whose anti-immigration policies and campaigns are racist in nature) or other racist organisations".
Speaking with journalists afterwards, Mr Kebede said Farage was a "pound-shop Donald Trump" who had "made a career out of dog-whistle politics", but did not label him or his party "racist".
Asked whether he therefore disagreed with the motion, he said: "I think there [are] an awful lot of racists who are getting involved in Reform."
Pressed on whether that included Farage, he said: "I think Nigel Farage is a right-wing populist."
Responding to the comments at a press conference in County Durham, Farage said Mr Kebede was a "self-declared Marxist" who was encouraging "indoctrination of teenagers in our schools".
He said the union leader was "somebody who is absolutely determined that our children should be poisoned at school, their minds should be poisoned about everything to do with this country, its history, what it stood for".
He added: "I'll make one thing very, very clear: if we win the 2029 general election, we will go to war with the National Education Union and all left-wing teachers' unions.
"People should be taught objectively, fairly and should be taught critical thinking where kids can make their own minds up what they believe and not be indoctrinated."
Reform MP Lee Anderson said the NEU had "shown its true colours", adding: "Rather than focusing on educating Britain's youth, it seems more interested in political indoctrination, silencing free speech, and spreading divisive rhetoric."
