As the dominant culture, it is not our place to decide to exclude groups of people based on a preconception.
I’m not sure progressives are the dominant culture in America, but regardless exclusion based on preconception is not the only kind of exclusion. You can exclude cultures based on behaviors that have demonstrated to lead to unacceptable consequences, and that does include white conservatives. It’s clear that liberals believe white, Christian conservative culture is at least partly unacceptable, even dangerous, and yet you insist it be tolerated. This seems, foolish. Especially since those conservatives seem hell bent on destroying your culture. It’s like refusing to remove a murderer from your home because that would go against the spirit of inclusion.
Every culture has blindspots. But none of them are absolutes. You tolerate the culture, and try to discourage behavior that is detrimental to the whole. Otherwise we’d ban most religions. Even western ones.
But what you’re describing isn’t inclusion, it’s passive assimilation. Discouraging behaviors you consider detrimental isn’t inclusion, it’s the opposite. Even if you are not excluding the whole culture, you are excluding part of it. I don’t think that’s a bad thing, but it’s not inclusivity and diversity, it’s promoting cultural homogeny, at least homogeny of some core principles. So, even if you don’t want to outright ban most religions, even western ones, because that would go against your core principles, you do want to “ban” (albeit not overtly) some aspects of those cultures.