Yes and no. As Marx argued, racism is a tool that divides the working class. Overcoming racism is essential in order to defeat capitalism. As Marx said of the English working class's views of the Irish:

Hence it is the task of the International everywhere to put the conflict between England and Ireland in the foreground, and everywhere to side openly with Ireland. It is the special task of the Central Council in London to make the English workers realise that for them the national emancipation of Ireland is not a question of abstract justice or humanitarian sentiment but the first condition of their own social emancipation.

To quote Robert Knox and Ashok Kumar's recent introduction to an issue of Historical Materialism:

Marx essentially bequeathed three points to later Marxists’ thinking about race. The first was that race and racism are deeply connected to capitalism’s spread internationally. The second was that racism is bound up with internal competition within the working class, and serves – both as a conscious project of the ruling class and directly via the labour movement – to undermine the basis for a revolutionary movement. The third was that Marx did not assign race or racism an independent causational force: it was clear that Marx did not think people were enslaved, exploited or dispossessed because of their racialisation, but rather owing to definite social conditions. The latter also points us to a significant limitation of Marx’s reflections: whilst Marx’s analysis did not ascribe any particular causational power to race, he nonetheless took for granted the existence of racial categories. As such, ‘race’ as a category was not subjected to the same historical and materialist analysis that both Marx and Engels would deploy in relation to other phenomena, and it was this task that later thinkers in the Marxist tradition sought to undertake.

But you are right that, of course, racism will also still exist after any revolution and will have to be at the forefront of the proletarian's mind.

For those interested, Knox and Kumar's article is an easy read and really helpful here: Robert Knox and Ashok Kumar. "Reexamining Race and Capitalism in the Marxist Tradition – Editorial Introduction", Historical Materialism 31 (2023): 25-48. The two special issues of Historical Materialism are here and here. Some articles are open access, but you can always email the author if you want the article.