No, you don't need genetic differences for racism.
In fact, in most European languages the words "race" and "racism" are talking more about nationalities than about genetically different population groups.
For example, if you read German articles from the 1920s, they often talk about the "German race", the "French race" or the "English race". In most European languages the word "race" fell out of use after WW2 and the American meaning of the word "race" was re-imported later on. But the meaning lives on in the meaning of "racism".
For example, in German a white person from Germany who hates everyone from France irrespective of their skin color is still a racist, while in the USA that wouldn't qualify as racism.
That's because neither the word "race" nor "racism" have a clear definition. "Race" is used entirely to discriminate "them" vs "us". So "race" determines whatever group people in a country want to discriminate against.
In the USA this was clearly a "we, the while ex-european people" vs "them, the black former slaves" and "them, the asians" and "them, the south americans".
So what would happen if suddenly everyone had the same skin color? People would just shift to the next best thing to discriminate.
Instead of discriminating against black people, just do what has been done in Europe for millennia: Discriminate against slavic people. (The term "slave" comes from "slavic", because it was so common to keep slavic people as slaves.)
And if nations, religions, languages and regions of origin would also disappear as things to discriminate against, then it would shift to the next thing: people who went to a different school, have a different education or best of all: other types of poor people.
The issue is that humans are heuristics-based beings. Prejudices the result of learning. I've had 5 crappy HP printers, so I conclude all HP printers suck. Some friends have had terrible experiences with Fiat cars, so I avoid Fiat cars. I read in the newspaper that Nestle is destroying the planet, so I eat something else.
The problem is that if this is applied to humans, they get unfairly judged for things that are often completely out of their control. The core mechanism that we humans function on happens to be severely destructive in this context. But that's also why it's hard to impossible to get rid of racism and similar forms of discrimination because they are so centrally embedded in how we humans function.
