Are there any rules regarding correlation between the variables used in a CNN?
In theory, convolutional and pooling layers should be able to account for this kind of collinearity. Convolutional filters will learn to extract the relevant information from your pixel data, and pooling layers significantly reduce their dimensionality, reducing multicollinearity as a side effect.

However, if you think multicollinearity is still a problem, you can apply some dimensionality reduction techniques. They work on image data as well!