I cannot see how you are following a Baysian framework at all.
First of all, the studies I cite are NOT "lived experiences," but hard statistics showing a clear bias in how black people are treated by police. When this aligns well with the personal stories and anecdotes black people have about racism, then the picture is quite clear.
You cannot treat evidence in isolation. Personal experience alone may not prove much, just like a footprint on the murder scene may not be strong enough evidence. But when you piece together several independent pieces of evidence, then you get a strong case.
When a large majority of black people report extensively about racism, there are many ways to interpret that. Your suggest is that it is just some kind of fluke, because personal experiences are unreliable. However here we are dealing with the law of of large numbers. It is simply highly implausible that everybody reports on this without there being anything to it. If you follow a Baysian framework, then this observations points to racism being probable. That everyone in a consistent manner reports racism while there is none, comes across as highly improbable.
And anyway there are countless third party observations written down by people who are not black, who also make the same observations. I make the same observations when looking at videos of interactions with black people by e.g. police offers. But we are to believe, this is all a fluke? That we all imagine the same thing. That is like suggesting we all have the same consistent distortion of realtiy. The mere suggestion comes across as deeply unreasonable.
As for self-interests and bias. We know the self interest and bias against black people have a very long history, because there was a strong economic incentive to deem black people as lesser than whites. The economically powerful majority has had an investment in it. I look at the civil rights period at the argument made then. People denied racism and systemic bias with exactly the same arguments you use today. There is nothing new under the sun. They also insisted that there was no racism and that it was just false perception. They argued that people like King, just fired up black people, making them believe in things that were not true. There is a clear belittling of black people here. The idea that they cannot think and reason for themselves. That some elites have told them that they are subject to racism and thus they start reporting it themselves.
Of course there is an implied racism in libertarian beliefs. That they deny it, doesn't mean it isn't. They suggest there is no systemic racism, or bias against poor people. That everybody has equal opportunity in principle. That the differences that exist in society must be the outcome of individual differences. Thus if black people are consistently poorer and have worse crime statistics than white people, then the only explanation is that on average, black people are simply worse people than white. Since society is excluded as a cause, it must be genetif inferiority at play.
That government most of the time makes matters worse comes across as borderline dogmatic fundamentalism. All through history government has made things better. In fact it has been very hard for society to improve without government making changes.
When there was feudalism and serfdom, then government action was required to end it. You could negative feudalism and serfdom with private charity. When there was child labour in the mines, then government had to make laws to ban it. Private charity or comapanies suddenly becoming "nice" was not going to change it. When people worked 12 hour days, then reducing that to 8 was not going to happen without government passing laws. When workers got exposed to hazardous material at work making them sick and dying, then government action was required. Before government setup food and drug administration testing the safety of food, then both parents and children got regularly sick and even died from bad food. Read up on the poison squad e.g. The list of government action which has improved our lives is so long that you got to be ideologically blinded to not see it.
If you live in a dictatorship, then you cannot end up in a democracy without government action. Government has to pass new laws and changes to create a democracy.
The way you write about systemic racism, makes it sound like libertarians are very afraid of aknowledging it because they fear it will cause government action. Thus there is an investment in denying its existence to hinder government action from happening. Given that they believe government action is always bad.
However I don't believe one needs to make many laws of actions which explicilty target black people. Rather I think racism is what drives a lot of the choices America has made as a nation. Ronald Reagan played extensively on racism when he cut welfare services. He knew white loathed the idea of "lazy poor black people getting free stuff." Likewise the extremely draconian American justice system has in large part been driven by a fear of the black man. That police are not held accountable for their actions is in large part because the white majority for a long time has wanted to keep black men in their place. You can just look at the history of policing in the South. I don't think people want cops to be held accountable, because they don't want to deprive cops of tools to take down black criminals. Dealing with systemic racism is in my view about reversing the whole Southern Strategy.
What you see are choices like making crack cocaine carry much higher sentence than regular cocaine because it was something black people typically sold and used. It is these kinds of laws which don't mention blacks by name explicitly but which is targeted towards them which needs to be removed. That is how I see you can deal with systemic racism. Remove or change laws which was meant to target black people. Reorient the prison system more towards rehabilitation. It is not hard to see why rehabilitation has no focus if people believe black people are just inherently bad or criminal. Sure this affects white people as well. But to many people, a criminal is a black person. Punishing criminals is thus a way of punishing black people in their view. It is just like when white talk about single moms on welfare. It is just coded language for a single black women on welfare. It is like when Reagan talked about "welfare queens."
