and how do I react next time they don’t greet me?
I started working at this department 3 weeks ago. I went into the office I now work at, greeted 2 coworkers I’ve already worked with, they looked at me, said nothing, kept talking to themselves.
How am I supposed to interpret that?
To me this is disrespectful, maybe you disagree?
Then, as I was working, I saw both of them staring at me. What am I supposed to do when that happens? To me this signals hostility and passive aggressiveness.
I separate private life from personal one but even I know that the least you can do is to greet your coworkers, unless you want them to quit.
Yes this is disrespectful.
My advice would be to stop greeting them until they notice you. Occasionally try again, but not every day.
In this case, you say “what is it?” to them. If they continue to stare at you wordlessly, you may escalate slowly to either violence or a report to authority.
Whether you decide to self-handle it or have authority handle it, if they continue to stare wordlessly at you as you try to communicate with them, you escalate to the point where it forces them to move.