Only a little over 10% of the respondents who opposed these programs opposed it because they thought it was inappropriate for government to do that sort of thing. More thought it was unnecessary, too costly, bound to fail, etc. By far the most common response was that blacks shouldn't turn to the government and instead help themselves.
With all this talk about Rand Paul and what he thought of the Civil Rights Act, it's important to keep in mind that he's joining a crowd that is motivated for decidedly non-libertarian reasons. We don't have large surveys, but the same is likely to be true of the Civil War. If there were genuine advocates of libertarianism using that argument to justify the Confederacy at the time, they were probably in the minority.