Of course it does.
An absence of direct evidence of what happened implies that we don't know what happened, not that your biases (or mine, or anyone else's) are justified.
It's not about biases; it's about what is likely to have happened.
His history of violent crime, as indicated by his criminal record, is necessarily a biased account. Criminal records only record the occasions on which he was violent, and was called to account for his violence. They don't record any occasions on which he showed restraint, politeness, or kindness, because none of those are crimes.
A criminal record records only crimes - duh. It still tells us a lot about his propensity to get criminally violent.
The only way that his criminal record could possibly be relevant, is in a world in which people are consistent, and can therefore be categorised into "good guys" or "bad guys". But that categorisation is nonsense. People are just "guys".
No, your idea that there is no difference between people is nonsense. Jordan Neely was a bad guy who attacked people for no reason. He broke an older woman's nose and orbital socket. Regular people don't do that.
I get what point you are trying to make, and it does have some validity. But only some.
Yes, human beings are complex. Yes, we are not 100% consistent. And yet, there are major differences in character between different people. And while prior behavior does not guarantee future behavior, it is still a good predictor for it, and the best one we have.
They're rarely consistent, and are under no obligation to conform with your belief that they will be.
They may be "under no obligation" but a person with a history of violence is still far more likely to get violent than somebody without.
Real people are inconsistent. Only computer and role-playing game 'non-player characters' are consistent. The problem many conservatives have is that they genuinely believe that anyone outside their immediate circle are non-player characters, and don't have the same complex and inconsistent behaviours as real human beings.
I do not know what "conservatives" think, but you seem to view them as NPCs yourself.

I.e. you are doing what you are alleging them to be doing.
As for myself, I understand that real people are complex and not "NPCs". That said, we all make judgments about people based on what they have done in the past. How do you decide who you put and keep in your circle? By their behavior. If a friend is consistently flakey, you will end the friendship. If they are consistently reliable, you will trust them more. You will not pretend that past behavior does not matter because real people are "inconsistent".
The only thing that Neely's history tells us with any confidence is that he got caught.
Because all people break random straphangers' noses and orbital sockets, but just never get caught? Is that your point?
I doubt there's a single human being in history who has never once engaged in unlawful violence.
There is a difference between maybe showing somebody during an argument, or having a fight on the schoolyard and breaking an older woman's bones in an unprovoked attack on the subway when you are pushing 30.
While nobody is perfect, people are not all the same either.