I have a question for someone who knows more about history than I do (which is just about everyone)

I don't really know a better place to ask this, so it's in the general chatter threads now. If it turns out this is actually super fucking offensive I'll take it down, but this question has been bugging me, so here it is.

I've been thinking a lot about the U.S.'s "separate but equal" laws, and about pictures I've seen of segregated water fountains, bathrooms, pools, etc. First of all, clearly not equal, so that's bullshit right off the bat. Second of all, and here's the question that's been bothering me, what was the logic there? What did they think was going to happen if black and white people swam in the same pool? I'm genuinely curious about why white people were so terrified by the idea of touching the same things black people touched.

Is there an answer, or does it just come back to racism being deeply ingrained in the culture of the time and white people panicking about everything?