Because everyone has some amount of racism whether they realise it or not but it still is not acceptable to display that racism. Sure having some racist thoughts isn't great but just like with almost every other unacceptable topic, everybody thinks about it sometime. It is only a problem when it becomes verbal/affecting others. That is why people are upset with him.
1) Polite people try to cover up their racism; it's not socially acceptable in the US. This is not the case in all countries -- I've been in other countries where certain levels are racism are really still A-OK. For instance, in some Scandinavian countries it's not unusual to have a housing contract that says the place can't be rented or sold to Roma/Gypsies. Few people see anything wrong with that -- it's something you just obviously wouldn't want to happen!
2) The professor should be better at their job (I say as a prof). I accuse students of plagiarism only if I have proof, and the last 4 times it's happened I've been able to highlight passages and provide the citation of the original paper, with the page number. Or I can show the student their peer's paper with the same exact sentences and typos. I'm sure it's plagiarism. If I can't prove it, I poke around. I ask the student to come in and describe their process to me, talk through their notes. This works. People crack, or they reveal their legit process. Sometimes that legit process includes a crappy first draft that got immensely better via four sessions with the Writing Center. Great. Sometimes their not-quite-legit process involves too much help from their girlfriend. Then we have a talk about what's appropriate and how they can rectify the situation.
Because the professor is in a position of power and they abused that power because of their biases. Prejudice is far more damaging when paired with power than without. It is injustice. If injustice is not worth moral outrage, what is?