Privilege at the individual level isn’t inherently bad or good, it just is.
For example, say you had a privileged upbringing: you were never hungry, didn’t have to work in highschool, and had money to participate in after school activities. That made it easier for you to get into a top school compared to someone without those advantages. That is not a sin or a flaw, and it doesn’t make you a bad person.
Now you can (and I would) say that this kind of privilege should be counteracted at the systemic level, by better funding public schools for example.
I don’t think those two ideas are in conflict.