There is a cop, in my city, who has a gadsden flag, blue line flag, and a gold/black ancap flag, on his porch. He also has nazi appropriated norse symbolism tattooed on his arms. These people exist, he is a walking joke, like I would have thought this was some sort of trolling, if I didn't know he was risking his job over the tatts. He eventually deleted his facebook, and nextdoor, profiles because of how badly he was being made fun of over it, once someone dropped a link to his profile on reddit. He was worried he might lose his job if all that stayed up. He did, eventually get fired, but it had to do with something other than his suspicious tatts, and hypocritical beliefs.

ancap thought is perfectly compatible with a privatized police force

Are you referring to a private police force because of the mention of the Thin Blue Line flag?

ancap thought is perfectly compatible with […] white supremacy

It depends what you mean by "perfectly compatible". An ancap would believe that the state shouldn't be able to prevent a person from being a white supremacist.

And the Gadsden flag is commonly understood as being against state interference, not other forms of oppression.

I agree. Perhaps my previous comment was lacking in clarity.

Edit: and while I agree that it seems like an odd combination, there are really plenty libertarians out there who think they need to buy out /bribe the local police force to get them on their side should things go their way.

I would be hesitant to refer to such an individual as a libertarian. At the very least, not without further information.

It’s only cognitive dissonance if you assume all people are equal and deserve equal rights and freedoms.

Correct.

A significant percentage of self-described […] libertarians believe all people are not equal - that there are good people, who will use freedom responsibly, and bad people, who will use their freedom to harm others, and it is the purpose of government (cops, sheriffs, border patrol) to protect the good people from the bad people.

Such an individual would not be a libertarian.

Such […] libertarians wave the thin blue line flag unironically and with complete ideological consistency, because they believe police brutality and oppression will be directed at those who rightfully deserve to be oppressed.

A belief in libertarianism and the display of a Thin Blue Line flag is no longer teetering on, and is now simply cognitive dissonance. They are mutually exclusive.

Uhm, lots to unpack here, but I think you are mixing things up. Yes, classic conservatives do a divide like that and there is a reasonable argument to be had about the existence of people "bad" people without getting into moral arguments.

But the libertarians do not make this argument. They literally argue that being bad, i.e. acting purely selfish becomes a net positive to society through the invisible hand of the market 🙄

If they support police than that is on the grounds of in-group thinking ("these are our guys") or more often purely utilitarian as in: "we pay them to protect our interests".