I built two strictly identical test sites in order to try to understand what happens.
The 1st one, with just the CSS optimization activated on Autoptimize:
http://autoptimize.wordpress-hebergement.fr
As you can see, the body background color is #e6e6e6 (go to the bottom of the page to see the background color)
The second one, just the same without any optimization activated on Autoptimize:
http://without-autoptimize.wordpress-hebergement.fr
And here, the background color is white.
Do you find something in it that could explain the trouble ?