And now the conversation with you is the last thing they heard about it. Maybe something will stick and plant a seed of doubt about the mainstream narrative. Even in conversations about topics that do not threaten hegemony, people do not usually change their minds immediate upon hearing new information. But people do change their minds all the time, just later in private and on their own terms.

The foremost problem with changing the mind of white western chauvinists really is racism which makes them unable to feel a normal amount of empathy. You explain about Palestinians suffering and they understand and believe you and it just does not trigger the normal human response of caring. So they seek explanations to justify their own failure as a human being to save face and imperial propaganda offers plenty. One countermeasure that just works and smashes through the lack of empathy is real human connection to affected people. But it's hard to implement as a general strategy.

The second big thing is instinctive fear to lose some of the material privileges they might have as a white liberal in the imperial core by going down the road of solidarity. The natural countermeasure would be raising working class solidarity and explain how their own struggles are interconnected.

Edit: One strategy, that has worked for me with white but leftist friends who are open minded and invested in our friendship is the following: After making clear, how much it matters to me and having a discussion, I cut the argument short and just give them homework. Ask them to just please read this theory. "Please just do this for me." Or to visit a local solidarity camp. It gives them time to change their minds in their own time. It worked on three people so far. Two of them said, they would never come to pro Palestine protest with me initially and later went multiple times. One even took night shifts at a camp.

Second edit: Actually I had to ask a friend to assign them the theory and answer questions, after they agreed, because I felt too triggered by their bullshit. So it wasn't easy or anything. And I feel lucky, that it worked multiple times. I was really scared to lose three good friends over this one after the other.

All this combined with internalized xenophobia

This guy doesn't know anything about the middle east or the us, but he feels compelled to have an opinion on it

When he feels like he messed up, his immediate thought is "I hated the wrong group"

Yeah, I broadly agree. I would phrase it as outside of their hobbies, interests, and work a lot of people don't have a lot of general knowledge and don't have any strong feelings about things they do know.

Are you sure that's really "crafting opinions out of thin air" like you say, or is that more just crafting public-facing opinions out of thin air? Because I'd think that someone saying whatever they think is socially appropriate in order to avoid confrontation, that that doesn't really preclude having genuine opinions, even if underdeveloped and unstable — it just means that their ideology sees the avoidance of social confrontation as the highest priority.