Did you read the linked article?
If so, could you be so kind as to speak to why you disagree with its unusually thorough and detailed legal analysis of the matter at hand?
The Shrek image may have been crude or vulgar. But in context, there is no serious argument Byrnes sent it to arouse anyone’s sexual interest, let alone that it satisfies the Miller test. Byrnes sent it to another adult, reportedly accompanied by political commentary describing Cirino as “Young Mussolini.” That’s protected political mockery, not obscenity.