The explicit purpose for segregation was to avoid the mixing of races, especially to separate Black men from white women.

The reason segregation and racial divide was so sticky in the South is that white people literally did everything in their power to not be around Black people. This was because Black America and White America - both in and outside of the South - functioned as two totally different places. Job postings would frequently include passages in the first few sentences or the last sentence reading "[insert word that I won't be using] need not apply" or something to that effect. Plessy v. Ferguson (1892 if memory serves me) held that governments can segregate public facilities based on race, and business owners were at liberty to refuse service to nonwhite folks. Thus, Black and white people usually didn't have anywhere public where they could be together.

Meanwhile, economic practices from the public sector (like the decision to not allow the VA to administer GI bill loans and the availability to utilities such as sewage, plumbing, etc), the private sector (like redlining), and from white society (such as community/HOA agreements/ deeds to property which made it contractually illegal to sell one's home to a Black person) made it so that white people were spatially distant from Black people - Black people could not afford to live in predominantly white areas, and when they could they couldn't get loans or mortgages, either because of unreasonable interest rates or because banks literally wouldn't lend to Black people. So, folks who somehow had the money to buy a house outright or somehow managed to get around the money issue could still be locked out of purchase because of laws/legal contracts on the books which literally made it illegal for someone to sell their home to you. This meant that some sections of towns/cities were virtually or literally completely all-Black or all-white. So, you would be unlikely to meet a stranger of another race on the street (especially when considering for much of the time period we're describe Black people were victims of lynching's at incomprehensible rates and would go out of their way to travel in spaces away from white people in the hopes they may be safer).

Basically, biological racism was the core of how (white) people in this time and place conceptualized social order and society. It was incredibly difficult for white and Black people to be in the same spaces, and when they were, it often was at the expense of Black people. If such relationships (platonic or otherwise) occurred, it was almost invariable occurred in private spaces, where the government, who by statue opposed them, or by the community, which looked at such relationships as inherently immoral and threatening to the established hierarchical order and would punish anyone who digressed.

If you'd like a book about this, one of my favorite works of public history is called Wilmington's Lie. It details the white supremacist coup in Wilmington, NC and a close reading will show you how the racist thinking which inspired Jim Crow impacted race relations even in spaces which were remarkably desegregated, making them incredibly hostile to people of color.