Does it bug you when people insult a person's past and think that person is still the person they were?

It depends. We should give people credit for their growth, it’s hard and it’s worth applauding. At the same time, sometimes patterns of behavior or habits can be hard to forget because they impact the people around us and it’s not so easy to earn trust again. It can go both ways, for me.

No. They’re often speaking out of their own hurt from something I did that I’ve repented of (meaning I’ve apologized and I don’t do it anymore, and that I’ve cleaned up the mess I made).

Or that I represent someone who hurt them.

I don’t purposely hurt anyone anymore. As much as is possible, I have cleaned up my part in it. Now they have the choice (and responsibility) to own their part of the problem. And I pray for them.

One of my daughters is like this. She’s very bitter.

No. If I hurt them in the past, I would expect them to bring it up and us to hash it out. I believe you have to own your past actions and hopefully show people whom you hurt that you have changed.

Or assume the opposite about about a person that is not so good?
Eventually, the truth comes out,good or bad Sometimes it takes a long time

My experience is that one is likely to repeat what one has done before, despite their good intentions. Unless they have demonstrated that they now act correctly under circumstances similar to what existed when they acted badly, I continue to doubt they will do what is right in the future.

How inaccurate is it? Sure, some people have changed and moved from their past, but many have not. I agree with @Bill1939 – past often predicts the future.

Especially at the first meeting.

No one’s perfect, but many people haven’t learned that. Or learned to look in a mirror.

For me, people like that are not my people and I let them go with love.

In order to move on from past discretions you have to accept you will be reminded of them, a good thing because you should never forget the lessons learned.

Until it is demonstrated otherwise, how else are you to assess an individual other than through his or her previous behavior?