Which PC narrative suggests otherwise? I'm not familiar which one pretends and relies on the exclusion of various slave trades, can you elaborate?
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.
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.
This isn't limited to Europeans, clearly.
Again though, these modern PC culture groupings that make reference to "white privilege" for all Caucasian looking people fall into the ignorantly ridiculous, or obtuse. I'm Eastern European, from the Balkans, my family and me were war refugees who never had much serious privilege in our lives but I've had people lecture me about white privilege as if I somehow have fault for an arbitrary genetic manifestation on the skin and am thus little different from any caricature of self indulgent wealthy, institutional white business men (not that there's anything specifically wrong with them either by the way).
Ironically, in my direct "privileged white" family, a paternal grandfather was a concentration camp inmate and a maternal great grandfather was an ostarbieter for the Nazis, deported to the Reich during the World War as.... a real-life 20th century slave.