There are different flavors of how people think of themselves as the cultural outgroup. The two examples I’m thinking of are (1) the type often claimed by racial minorities, where there’s systemic racism against them even if it’s not explicit in the law, and (2) the type often claimed by devout Christians, where there’s a sort of quiet effort to make life harder for them or even snuff them out by outlawing and erasing their symbols and enacting laws exactly counter to their beliefs.
I think my mind went to these two examples because they might be exact inverses of each other. In the first case, it’s difficult to define exactly where systemic racism occurs, but because the heritages of racial minorities don’t permeate or provide the foundation of Western society the same way, say, classical Greek thought, Shakespeare, and Christianity do, they feel a sense of being forever outsiders anyway, which provokes the feeling of being systemically discriminated against.
In the second case, there’s little question that Christianity is deeply embedded in Western society, and it’s still not hard to find Christians basically anywhere you might go, or see Christian values and symbols reflected all over our culture — even granting claims that there is an effort to erase them. But this alleged effort is still something many Christians perceive, and they can point to dozens of specific examples.
Another way to illustrate the difference might be this: lots of white people want a black person on their team at work, or in their neighborhood, or in their friendship circle, or whatever, because that means “diversity” and diversity makes them feel great — and blacks in these situations are typically treated very well (barring offensive misunderstandings, etc.) but when blacks become the local majority then whites start to get anxious and leave.
Inversely, Western non-Christians are accustomed to living in a Christian-dominated world and were basically tolerant and even supportive of it (how many non-Christians, or at least non-believers, still celebrate Christmas and Easter?), but once they start to sense that Christians are becoming the local minority, non-Christians become emboldened to do things like take down nativity scenes, ban the ten commandments, take the word “God” off the currency, etc.
So on the one hand you have a sense of not being let in and on the other hand you have a sense of being pushed out.
This is still a little fuzzy and I’m not sure it makes sense. It might not. Or it might and I’m just not explaining it well at all.