Prejudice is prejudgment, or forming an opinion before becoming aware of the relevant facts of a case.
How exactly does this differ from a Bayesian prior?
The Pygmalion effect, or Rosenthal effect, is the phenomenon whereby the greater the expectation placed upon people, the better they perform.[1] (Or the observer thinks it would be so!) A corollary of the Pygmalion effect is the golem effect, in which low expectations lead to a decrease in performance. (wikipedia)
Um, there is a lot of debate about whether this effect exists.
Given the nature of the website it would make sense for you to analyse the relationship between what you are saying and Bayesian priors if you want to convince people.
Or, it starts from a poor probability assignment in the first place.
Basically, prejudice as a bad thing is poor Bayesian reasoning, not all Bayesian reasoning. Unfortunately, many opponents of prejudice would insist on throwing out some good Bayesian reasoning as well.
How exactly does this differ from a Bayesian prior?
Um, there is a lot of debate about whether this effect exists.
Am I not allowed to call it “prejudice” if it’s like a Bayesian prior?
It’s not a matter of “allowed”.
Given the nature of the website it would make sense for you to analyse the relationship between what you are saying and Bayesian priors if you want to convince people.
In practice, it differs in that once an opinion is formed it’s sticky and contrary evidence tends not to result in updating.
Or, it starts from a poor probability assignment in the first place.
Basically, prejudice as a bad thing is poor Bayesian reasoning, not all Bayesian reasoning. Unfortunately, many opponents of prejudice would insist on throwing out some good Bayesian reasoning as well.
The key in discussing prejudice as something bad is to distinguish it from general Bayesian reasoning, which is good if done right.
Your question points to the failure of the OP to distinguish between good and bad Bayesian reasoning.