Obviously, it is the idea of segregated fountains that is objectionable, and would remain objectionable even where facilities were in fact "equal" in water quality, sanitation and appearance.
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I also recall that there was a chain of discount gas stations that advertised better service and lower prices in East Texas called Billups. They had SIX restrooms. Three on one side for White Men, Colored Men, Mexican Men, and three on the other side for White Women, Colored Women and Mexican Men.
This was before the term "Hispanic" was used anywhere. Also, back in the 1950's everyone was sure that all nasty diseases were spread by toilet seats. This wasn't true, but people still insist on the possibility that they could get the clap or syphilis from the plumbing without really trying hard to do so.
The 1954 Supreme Court decision ruled that even if the facilities were identical (which was closer to being true in Topeka, Kansas than in the South) it was still unjust, because it implied that the races were unequal intellectually.
The usual assumption is that people should be given the freedom to do as they please unless there is a demonstrable reason why their doing so detracts from the rights of others.
If Adam marries Steve, precisely how does this detract from the mariage of Bob to Carol or Ted to Alice?
I dare you to find one valid reason. Double-dog dare you, in fact.