The thing about white privilege, male privilege etc is that they aren't things you can change. They sit alongside, but are different from privileges like economic or class ones.
I do think its sad that people, usually white people, see being told they have white privilege as an accusation and get defensive. Of course being white does not negate other disadvantages you may have, but it doesn't add an extra one.
In the US, if you look at death row cases, the vast majority of prisoners on death row are black. White prisoners are less likely to be sentenced to death for the same crime. That is white privilege at its best.
White/male privilege (and others for that matter) bring unconscious bias to the table. It's the people who are obviously not male/ white getting fewer job interivews/opportunities. It's also a difference in how safe people feel. It's in "silly examples" like women being assumed to be the PA or asked to make coffee in meetings. It's black men being more likely to be stopped and searched.
And surely you have to be blind not to notice that this is endemic? What's that statistic about more men called John running FTSE 100 companies than women? And of course, we're not seeing any particularly meaningful number of POC in these positions either.
I used to live in SW london. Local Waitrose was staffed by largely majority BAME individuals. But the managers were all white? Is that just coincidence? I don't think so.
White privilege doesn't mean you've had it easy but has many people have pointed out, being white doesn't make your life harder. You may well be discriminated against because of your physical/mental health, because of your sexuality, because of your sex, because of your education, because of your upbringing. But you won't be discriminated against because you're white.
[oh, and I think there've been a few examples of white people going into largely BAME communities and experiencing hostility as an example of why white privilege doesn't exist. Those are, frankly, irrelevant. In those situation, sure, being white is working against you. But white privilege refers to your experience in society overall. If we said it doesn't exist because in 0.01% of the time in 0.01% of situations it doesn't, we are deluding ourselves."