It does a disservice to the facts of apartheid to compare the US in 1964 to SA at the same time. While, yes, there were many many racial problems in the US, there were no race-based federal laws. The Civil Rights Act was passed to prohibit racial laws at the state level. Meanwhile, in South Africa:

All citizens had to carry a card identifying their race. (Population Registration Act)

It was specifically legally allowed to segregate public facilities (parks, hospitals, transportation, etc.). In addition, facilities were specifically allowed to be unequal for different races or even non-existent. (Reservation of Separate Amenities Act)

Property was legally divided by race and you could only live in areas alloted to your race. (Group Areas Act)

Federal law controlled which jobs you were allowed to hold based on your race. High skill jobs were reserved for whites and blacks were prohibited from holding them. (Mines and Works Act, Native Building Workers Act)

Blacks were legally prohibited from striking or forming unions. Whites had no such restriction. (Native Labour (Settlement of Disputes) Act, Industrial Conciliation Act)

Schools were legally segregated by race, which led (either intentionally or not) to radically inferior schooling for blacks. In the 70s, per capita spending on black education was one-tenth of the spending on white. (Bantu Education Act, Extension of University Education Act et. al.)

It was a federal crime, punishable by up to five years in prison to engage in inter-racial sex involving a white person. Inter-racial marriage was likewise outlawed. (Immorality Act, Prohibition of Mixed Marriages Act)

And this is just the beginning. There were dozens of other pieces of legislation that specifically encoded race-based selection into federal law. It's astonishing how horrendous South Africa was in a time where most other developed countries were what we think of as "modern".

There is nothing modern about the way the US treated race politics in the 1960s. It was appalling and a lot worse than many other countries - South Africa being a notable exception. It still puzzles me the amount race comes up in American TV shows. They are loaded with lame race based jokes which indicates to me that all still isn't right, and how could it be when my parents' generation can remember events of the 1960s. I live in New Zealand, and it would be untrue to claim race and racism aren't a problem here, but I think that the situation is slightly better although we have appalling stats for Maori and Pacific Islanders where health, life expectancy, poverty and education are concerned. I could be wrong but it recall reading that the Maori are the worlds most imprisoned race.

The modern prison system in America is provably racist, devastating to black communities, and legal.