You sound like a lot of my relatives OP who argue when I point out that as white heterosexual folks they are privileged.
They don't understand that while yes, a white person can be poor and indeed have a thousand different problems just the same as any person of any ethnicity, the fact is that being white will NEVER ever be a problem for them. It just won't. So while A may have the exact same problems as B if A is white then she will still be more priviledged than B because while they are dealing with the exact same problems B has to worry about racism and all the problems that can come with being a minority which A doesn't have to deal with, it is THAT simple.
That being said privilege come in all shapes and form I am a mixed race queer woman for example, so far from what people consider priviledged in term of "race", sexuality or even sex yet I still feel extremely priviledged and still enjoy a lot of privileges that many people don't have access to.
As someone from a powerful European country I get to travel and can enter and immigrate to other countries with ease and have access to ALL the privileges that come with being European.
When I go to the airport with my European passport I am fully conscious that despite being the exact same person I would be having a fully different experience/treatment if I was to use the passport from my other nationality (think poor country), THIS IS PRIVILEGE, being seen as "safe" when passing immigration because I am using the "right" passport and this is a privilege I am very conscious of profiting from. There is nothing wrong with being privileged, nobody got to pick their skin color or being born male etc... but not acknowledging that being born a certain way (be it white/straight/male) brings up some advantages/privileges or on the contrary disadvantages is ridiculous and only adds up to the problem and divide between people.