What, on Earth, is your point? During the exact same time period, there were very liberal Democrats who swept civil rights under the rug (FDR) and very conservative Republicans who openly called for civil rights legislation (Coolidge), which is my point: you can't just put civil rights on a left-right axis. It crossed party lines and ideological ones, as well. You have just simply decided through any number of lazy rationalizations that supporting civil rights is "liberal" (I would guess some form of Blacks are liberals now, so liberals - regardless of party - must have been the only ones fighting for them or the comical conclusion that because you are a liberal and you would have supported civil rights that it must be an inherently liberal view).
There were liberals and conservatives who supported and opposed civil rights all throughout the movement's history; to decide supporting or opposing basic civil rights is liberal is PURE conjecture. Period.