Whites–especially whites of my generation or slightly older–were explicitly taught (as kids and sometimes as adults) that there are no differences between racial groups; that all racial groups are friends; that it’s a small world after all. Our celebrities held concerts encouraging us to donate money to starving children in Africa, because, “We are the world.” We were promised a future of inter-racial harmony, where racial differences meant nothing more than liking tacos or needing less sunscreen.
Whites often fail at being racially inclusive, but they generally believe that they should be.
So it is generally with some surprise that whites learn that other people do not think the same thing about them. That a white person who marries a black person, attends a black college, dresses/styles her hair like black people, and devotes her life to the advancement of black causes might actually get rejected by other black people just because she isn’t black. Whites who have an interest in American Indian things, particularly religion, have another fine line to walk. You may watch respectfully, but you cannot join.
Some religions are very open to converts; Christianity in particular. Christians have trouble understanding that other religions might not be open to converts; other people might not want them.
As I see it, there are two main reasons to police the boundaries of a group: either because there are some benefits associated with being part of the group, like getting a job because you graduated from a particular school; or because you really hate people not in your group, like feminists who hate men so much they won’t let trans* folk into their gatherings.
Both of these notions go against white expectations. The anti-racist ideology teaches that there aren’t benefits associated with being non-white (that’s why it’s called white privilege, not black privilege,) and our generally cheerful assumption that we are all supposed to be friends, regardless of race.