Cleburne was probable the most dedicated and objective Confederate in the war, and stated that if the south lost the war that the southern history would be written for them. He also stated that he did not care one whit for the negro whether he was a slave or free did not matter to him. He was a pragmatic man who saw the situation as it was and so stated his position many times without regards to what others thought.
This straight forward speech about arming the slaves cost him the command of the Army of the Tennessee which he should have been commanding instead of Bragg. So I am really sure that Cleburne was following the lead of popular opinion when he suggested that the slave should be armed. Like a fish in a pickle dish he was following popular opinion.