Why do we have to remove most common words for text analysis?
The simplest way to explain why it may be advantageous to remove the most common words is that they don't give us much information. In your case of classifying racist tweets, words like "and", "a", "the", etc. don't help the classifier and may act as noise which negatively impacts performance.

I would not say that the removal of the n most popular words will guarantee that the model will be more accurate, but it is a parameter you can explore. Outside of complete removal of the most common words, you may want to look into techniques like subsampling.