MMM
That doesn’t sound like “privilege”, it sounds like “preference”.
When the preference is strong enough that it affects hiring decisions, whether you're even welcome in the restaurant at all, whether people think it's safe to have you living on the same street, the perceptions of a jury, etc. it does translate into an advantage, privilege, asset or whatever we want to call it.
Do you honestly think that black people would not also express an “immediate acceptance” for other blacks?
You're familiar with Washington DC, right? Why do you think a white boy like me couldn't get served in that particular restaurant?
Would you call that “black privilege”? Don’t you think those blacks might share something more than skin color?
People are people and they all have preferences. A great many people (apparently) don't seem to understand when the preference crosses the line into a prejudice.
There was a recent article in Scientific American, authored by twelve medical professionals which explained how initial reports of George Floyd's autopsy misused medical terms to make the police appear less culpable.
Look at how many people not only bought into it, but embellished it further, to the point where it morphed into the claim that Floyd was in a drug fueled rage which left the police no choice.
I'm not saying this was necessarily racial prejudice, as there are people who will reflexively defend the police no matter what they do. But either way, it is still food for thought.