“What will it mean in the long run if my white children don’t see and befriend people who come from different racial backgrounds?”
Not a thing. I grew up in a town of less than 10,000. From kindergarten through high school there were no blacks in our community, not one. A few Indians from the reservation and a handful of Mexicans was as ethnic as we got. The first black people I ever met were in boot camp. That included several of the drill sergeants so I did the best I could to get along with everybody. I still do.
Whites, Blacks, Filipinos, Polish, Jews, poor Southern Whites who couldn’t sign their own papers, college grads and big dumb oafs from all walks of life, thrown together in an old wooden barracks for two months, sleeping cheek by jowl in metal bunk beds. Tolerance and stand your ground, you learned both. I don’t know why people make such a big out of it.
You might be interested in my experience since it has some parallels. I grew up in the city of Birmingham, Alabama. The city and the state were very much racially divided; there were many blacks and some Hispanics but they stayed in their section of town and we stayed in ours, i.e., there was an understanding. Every one of my classmates from kindergarten through high school was white, and by that I mean no blacks, no Latinos. The only time I interacted with blacks and Latinos was in the three years I served in the U.S. military. When I got out I returned to Alabama and went through college. Again, no blacks, no Latinos, straight through graduation in 1966.
In other words, your experience was based on living in an all-white community whereas mine was based on living in a segregated community. Of course, it's no longer that way. I think the colleges in Alabama integrated maybe two years after I graduated.