Note: I live in Romania and my answer will be quite localized
"White privilege" concept is virtually unknown in Romania (never heard of it on local media, from friends, only from Politics.SE). This does not mean there is no discrimination, discrimination against Romani people. being a good example:
Racism is mostly directed against the Romani people, the country's
third-largest minority, who are routinely discriminated against by the
state, local authorities and private enterprises, in matters of
housing, employment and education.
Regarding a comment on OP:
in Eastern Europe who obviously didn't benefit from slavery
Actually there was slavery in Eastern Europe and some argue that ending it was not done properly, thus many problems related to discrimination and their integration:
Slavery (Romanian: robie) existed on the territory of present-day
Romania from before the founding of the principalities of Wallachia
and Moldavia in 13th–14th century, until it was abolished in stages
during the 1840s and 1850s, and also until 1783, in Transylvania and
Bukovina (parts of the Habsburg Monarchy). Most of the slaves were of
Roma (Gypsy) ethnicity
Following the abolition, there were attempts (both of the state and
private initiatives) to sedentize the nomads and to integrate the Roma
people into the Romanian society, but they had a rather limited
success.
I would say that “white privilege” virtually does not apply to some Eastern Europeans (at least not to Romanians). In fact, this article explains why racism is quite low (except that against Roma people):
(...) it really shouldn’t be interpreted as racism. In fact, you may
find that Romanians hold fewer racial stereotypes about blacks and
Asians than Americans do, simply because there are almost no people of
those races living in Romania and there are no cultural narratives
defining what PoC are “supposed” to be like.
[...]whites in Western societies enjoy advantages that non-whites do not experience[...]. White privilege denotes both obvious and less obvious passive advantages that white people may not recognize they have, which distinguishes it from overt bias or prejudice. These include cultural affirmations of one's own worth; presumed greater social status [...] also implies the right to assume the universality of one's own experiences, marking others as different or exceptional while perceiving oneself as normal.