If any of our board regulars were involved at the time I'd be interested to know if this impression is actually correct.
I was about five years too young to be actively involved, but yes, my impression at the time was that the white folks marching in the South were not particularly churchy and were left-leaning. That was the FBI's impression, too, as they tended to equate them with Godless Pinko Communists and such. Quite a few of the non-black "names" in the civil rights movement were Jewish, too: of course, Jews were still fighting "redlining" and other forms of discrimination themselves even into the 60's.
I'm kinda proud to say that my Presbyterian minister father preached against racial discrimination and habitually wore an "equality" lapel pin in 1960 or so - in Arkansas.