[Libertarian353]

According to the white privilege idea, whites do not face any type of racism.

Not necessarily, it means that the institutions in white society will always favor those who are consider white at the expense of non-whites(Historical Irish/Blacks/etc). Whites then and now live in probably worst conditions compare to certain Black cities, that doesn't mean they aren't favored. Economics means nothing, the idea is "Only blood will tell".

Also you forget the history of our culture and mistreatment of Scots/Irish/Britons when our forefathers came to Britain. Again, the greatest racism whites face is from other whites.

For example, can a white person get beaten up or discriminated against at an institutional level on the basis of their race?

Yes, consider the anti-Irish/East European sentiment in Europe. The Yugoslav wars is a perfect example of whites being oppressed.

I ask this, because maybe, in the eyes of white privilege theory advocates, violence and discrimination against whites would not be classified as racism.

White privilege is a first world concept that only accounts for Western nations compare to Eastern White ones. Manly America is the greatest example.

Because of course, whites cannot experience racism in the West due to historical context and the structure of Western societies.

Racism according to certain Black power organizations is an Institution+Discrimination. The quote say it best : “If a white man wants to lynch me, that's his problem. If he's got the power to lynch me, that's my problem. Racism is not a question of attitude; it's a question of power. Racism gets its power from capitalism. Thus, if you're anti-racist, whether you know it or not, you must be anti-capitalist. The power for racism, the power for sexism, comes from capitalism, not an attitude.” Stokely Carmichael.