White non-Jews do not see Jews as white
Modern definitions of racism focus on the oppression of one racial or ethnic group by another on the belief that one is superior. Using this definition, Jews would not be considered white, even if they visually appear to be. There is a long history of anti-Semitic and oppressive racist actions against the Jewish community around the world.  Those who define themselves as the ultimate deciders of whiteness, white supremacists, often exclude Jews from that group due to both their religious and ethnic identity. White non-Jews do not consider Jews to be white, and they are not afforded all of the advantages that white privilege affords white people in Western society. While Jews may be closer to whiteness than other racial and ethnic minorities, they are still excluded.
Racism is considered a social construct that is based on visual representation. While being Jewish is an ethnoreligious identity, it is not the same as saying one is Chinese or Sri Lankan. There is no distinguishing skin color or other visual factors that distinguish Jewishness or Jewish identity, and by nature of this, there are many light-skinned Jewish people that would be considered white by virtue of their skin color alone.