Another possibility could be that the Barrow gang sees the Civil War as an opportunity to lay low/disappear and takes advantage of that.
I wonder if Bonnie and Clyde would be as well known ITTL. It seems like the outbreak of the Civil War would butterfly a good deal of their activities in 1933-34. For instance, it seems possible there wouldn't be the raid of the Joplin apartment the gang briefly rented, which led to the discovery of undeveloped pictures of the couple that would play a significant role in their fame in OTL.
I remember a quote, I believe Michael Albert referenced it in his memoir
Remembering Tomorrow, something a leader in the historical Black Panther Party told him during their hey day, that "Many of us went from pushing dope to pushing
The Little Red Book, and we do it in much the same way." (I could be misremembering the source though).
I think this is instructive, and it's something often overlooked. Many people from the marginal sections of the working class are often the first people radicalized. They also live in precarious situations that often mean a life of crime. Though obviously not every criminal from OTL is going to turn out to be a revolutionary ITTL. Clyde Barrow might have been the sort of person to go into the Texas prison system for petty crime ITTL and leave preaching
State and Revolution in 1932. It's also highly unlikely he'd end up meeting Bonnie in similar circumstances to OTL.