Any person who negatively and unreasonably critiques another person based on ethnicity, race or skin colour is a racist. This applies even if those opinions are not voiced.
Of course this means that any person could potentially be a racist and we may be totally unaware of their views.
I've noticed people from a minority background are often the very worst racists of all, yet they are quick to point the accusatory finger at cracker whities.
Edit: I see you claim there are no racial slurs for a white person, yet I had already listed two in the answer, being whities and cracker
Here's a few more from the supplied link:
(Indonesia) White people; literally, "albino", but used in the same way that "colored" might be used to refer to a black person to mean any white person.
Mildly derogatory term used by African Americans, mainly in the 1960s and 1970s, to refer to a white person (from James Baldwin's play, Blues For Mister Charlie).
Coonass or coon-***
(U.S.) a Cajun; may be derived from the French conasse. May be used among Cajuns themselves. Not considered to be derogatory in most circumstances.
(U.S.) Derogatory term for whites, particularly from the American South.
(Thailand) any white person.
A derogatory term used to describe white people, especially older white men - based on the appearance of their faces.
(The Americas) Non-Hispanic U.S. national. Hence Gringolandia, the United States; not always a pejorative term, unless used with intent to offend.
(AUS) Aboriginal (Koori) term for white people – derived from Governor / Gubbanah
Gweilo, gwailo, or kwai lo (鬼佬)
(Hong Kong and South China) A White man. Gwei means "ghost". The color white is associated with ghosts in China. A lo is a regular guy (i.e. a fellow, a chap, or a bloke). Once a mark of xenophobia, the word was promoted by Maoists and is now in general, informal use.
Offensive term for a white person.
Usually not offensive, can be derogatory if intended to offend. Used by modern-day Native Hawaiians to refer to anyone of European descent whether native born or not. Use has spread to many other islands of the Pacific and is known in modern pop culture.
(U.S.) A central Central European laborer. It originated in the coal regions of Pennsylvania and West Virginia, where Poles and other immigrants from Central Europe (Hungarians (Magyar), Rusyns, Slovaks) came to perform hard manual labor on the mines.
Mangia cake / cake (Canada)
A derogatory term used by Italian Canadians to disdainfully describe those of Anglo-Saxon descent (from Italian, literally 'cake eater'). One suggestion is that this term originated from the perception of Italian immigrants that Canadian bread is sweet as cake in comparison to the rustic bread eaten by Italians.
Medigan / Amedigan (U.S.)
Similar to "mangia cake". A term used by Italian Americans to refer to Americans of White Anglo Saxon Protestant descent, Americans with no discernible ethnicity, or non-Italian Americans in general. Comes from Southern Italian pronunciation of the Italian word "americano".[self-published source]
(U.S.) a white person, unknown etymology.
A person from the State of Arkansas, used during the great depression to describe farmers from Arkansas looking for work else where.
A person from the State of Oklahoma, used during the great depression to describe farmers from Oklahoma looking for work else where.
(U.S.) a white person (southerner). This word was coined in the 19th century by Southern blacks to describe poor whites.
Offensive term for a white person.