I see it all the time in other people, I probably do it now and then too, but not thinking of an example right now. I do sometimes assume someone else is thinking like me, and might find out later I assumed wrong. That’s a form of projection maybe. Like when I have a disagreement with my husband. When I react to something he says, because I’m assuming his feelings based on how I feel.
My husband’s family has several members who I accuse of projection on a regular basis. It often is intertwined with hypocrisy. Like they accuse other family members of not being involved enough or not being in touch enough, when they don’t do anything to reach out either. In many instances they do much much less than other family members. This has been aimed at my husband and me as an on and off theme, but they do it to others also.
One of the classics in projection is an SO worrying and accusing their partner cheating when they do it themselves. They might get ridiculously possessive and controlling. I’ve seen this more than once, but haven’t dealt with it.
In politics today in the US the politicians use so much projection it’s mind boggling. Trump is a master, but not the only one. He accuses other politicians of the very things he does. It’s like calling witch.