Of course you see yourself differently as an "Eastern European" - Those distinctions don't translate to the US because when juxtaposed with darker skinned people (particularly the Descendants of Slaves in the US), the differences between Europeans becomes negligible.
Eg - When the Irish/Italians immigrated here in the 20th century they were initially seen as "other" but after a few decades "graduated" to white. So yes you do benefit, even if you don't realize it.
No. Whatever qualities, privileges or detriments that ignorant others ascribe to my skin color are not my fault or my responsibility to feel guilty over. This applies in all cases for anyone of any color.
What's more, your simplistic, ignorant color-based dismissal of an entire and enormous range of historical, cultural and personal history differences between certain eastern Europeans and certain other Europeans is no less insulting than the kind of low key racism that some people apply by labeling all blacks or brown-skinned people the same. The differences in both cases are emphatically not negligible. That you openly think this way is likely only because it's been instilled as politically acceptable. It sure as hell has no real merit.
That some so-called progressives often think this way today is a sad reminder of how old stupidities can come full circle to infect new generations.
In a functional sense when compared to darker skinned, non European people; in the US specifically, European cultural differences are far less significant as they are in Europe.
Eg - When the Irish/Italians immigrated here in the 20th century they were initially seen as "other" but after a few decades "graduated" to white. So yes you do benefit, even if you don't realize it.