Credit to DedicatedAcct

From a sociology dictionary:

The attributing of characteristics of inferiority to a particular racial category. Racism is a specific form of prejudice focused on race.

http://sociology.socialsciencedictionary.com/Sociology-Dictionary-R-1/racism

Here's another one:

Racism is the perception and treatment of a racial or ethnic group, or a member of that group, as intellectually, socially, and culturally inferior to one’s own group. It is more than an attitude; it is institutionalized in society. Racism involves negative attitudes that are sometimes linked with negative behavior.

http://sociology.about.com/od/R_Index/g/Racism.htm

And another one:

The belief that one race is supreme and all others are innately inferior.

http://highered.mcgraw-hill.com/sites/0072435569/student_view0/glossary.html

The source of the fringe definition that you claim predominates "most sociological discussions on the matter:"

As near as I can tell, the formulation "Racism = Prejudice + Power" originated in a book by Pat Bidol in 1970. Titled "Developing New Perspectives on Race," in it Bidol explicitly makes the formulation as stated and then uses this definition as the basis for an argument that in the United States Blacks cannot be racist against whites, they can only be racially prejudiced against them. This makes an important connection that matters as far as this particular nonsense is concerned, which is that this stipulated definition exists as an excuse to defend members of racial minorities against accusations of racism and it has always existed for this reason. The definition was largely popularized by Judy Katz, who referenced Bidol explicitly, in her 1978 book "White Awareness" which presented a course of counter-racist training for organizations. The book was highly influential and through it the formulation, for those who were searching for such a tool with which to deflect accusations of racism, gained popularity.

http://www.wetasphalt.com/content/why-racism-prejudice-power-wrong-way-approach-problems-racism

What you've done is picked a very narrow definition from a social movement from within sociology and applied it for the very same reason that it was invented in the first place: to create a semantic (and therefore meaningless) argument in order to defend your own bigotry while simultaneously decrying bigotry directed at others (perhaps yourself). There is no consensus whatsoever in the field of sociology that racism has any qualifier with regard to which races the term can apply to. Nor are there any non-racial qualifiers such as privilege or power because they are irrelevant with regards to racial discrimination and are relegated to the other types of discrimination, as they should be. Many many reject your definition outright because it's actually racist according to the standard definition. Now, if you want to qualify racism, you can do that all day long. Racial discrimination is what it is, but if power and privilege are important to you, they should be discussed parallel to each other, not one arbitrarily negating the other. Further, the new definition has no argument backing it. It's simply an assertion which is either accepted or rejected without reason. However, there are plenty of good arguments which preserves the original definition to the exclusion of incorporating power as a necessary qualifier for racism.

Keep in mind that the argument is semantic. You'd have to redefine several other words as well to try and make any kind of ideological separation. For example, even if there was a consensus that accepted that somehow that the word "racism" can't apply to instances of racial discrimination against white people in the United States, it still doesn't make it not racial discrimination and it still doesn't make it not wrong. It only means that we don't accept the word "racism" as applied to what used to be called racism with consideration of a majority population. It's an intellectually bankrupt argument and I wouldn't make it if you want anyone to take you seriously. It shows that you're willing to "win" using reasons other than ideological fortitude and as such can be perceived as an admission that you believe that your own point is fallacious if not outright incorrect.