Judging blindly- making assumptions or conclusions about a person without knowing them
Doing something blindly means to do something without having enough information. To judge blindly implies that you judge someone without having enough information.
Prejudging is probably what you're looking for.
Prejudging means to judge someone/something before knowing or having enough information (the prefix pre- also indicates that).
Cambridge English dictionary defines it as:
to form an opinion about a situation or a person before knowing or considering all of the facts:
In your example,
"So you're obsessed with rocks," Mary judged blindly.
Presumably, Mary made that statement without having enough information, so you could say:
"So you're obsessed with rocks", Mary prejudged them.
Here's a recent example from Fox8:
“On the heels of the Ahmaud Arbery tragedy, there aren’t any good reasons for an adult to prejudge an 11-year-old girl, wrongly accuse her of a crime and then assault her as she picked up her grandmother’s mail.”
Compare it with your example:
Prejudging/prejudgment can/will lead to injustice.
In your third example, you could replace 'blindly judging' with prejudging.
You have only known him 5 minutes, yet you are already blindly judging him.
A has known B for 5 minutes and is making up something about B without having enough information, you could say A is prejudging B.
Here's a good example from OregonLive:
ARIES (Mar 21-Apr. 19): Get to know someone. Shooting the breeze or traveling with a new acquaintance will allow you to find out more about what makes them tick. This knowledge is more valuable than prejudging others solely for their appearance.
Someone who prejudges could be described as prejudger.
If someone judges unfairly, you could say they're misjudging.
You could also use presumption (noun).