It's the coon skin caps.
When fighting in the revolutionary war, the cajuns could be identified by their raccoon caps - with the tails. So naturally they were wearing "coon asses" and could be identified as such.
This was particularly important for folks who had no uniform or other means of identification in battle. It was important to know who was on your side and who was not.
"A small group is emerging from the brush ahead. I got a clear shot."
"Don't shoot! Can't you see them thar are a bunch o' friendly coon asses loyal to the cause?"
The coon caps helped save their lives and were a de facto uniform. It was mildly derogatory, but it emerged from a real need for identification.