The HOA exists to protect common property values by enforcing common decency. I can understand their desire to prevent "eyesore" dishes. However, federal law says that they can't (for the most part) prevent dishes.
When I moved into my neighborhood with a fierce HOA, they mentioned that any dishes would need to be approved by "the committee." The committee chairperson told me flat out, "We can't prevent you from installing a dish." However, they did suggest that I put it on my chimney or the eaves of the rear of my house rather than on a pole or in the front yard. My dish is on the eaves of the rear corner of my house. They also send me a nasty gram in the mail when I don't edge or mow my lawn in reasonable time. I comply--no drama. :up