So to start this post, here's a popular sentiment:
I have to be honest. I'm getting tired of the common complaint that white people can't have white pride the same way minorities can. We can. I am perfectly happy and proud to be a white male.
But that's different from a white pride demonstration. A pride demonstration by a given group is meant as a response to societal oppression and shaming. It demonstrates to "The Man" that he's not going to keep them down. Even today, despite all the rights legally granted them, black people, Asians, Indians, Latinos, etc. are pigeonholed into some set of expectations and then socially punished for not abiding by them. And there is still plenty of racist behavior out there, the rhetoric of which suggests that the victim should feel like less of a human being for his/her minority status.
That is why minority groups have pride demonstrations. They are part of the ongoing struggle for equality not just in the eyes of the law, but in the eyes of society. Just like standing up to the school bully is more effective than avoiding him, so is demonstrating to "The Man" more effective than just ignoring him.
And that is why white pride demonstrations aren't usually appropriate. Generally speaking, the vast majority of white people do not have a problem with societal oppression and shaming, so for most of us, a demonstration would serve no purpose. It's not racist. It just mocks the whole concept.