They similarly hate ham radio antennas, but there are federal laws that mean you can do it anyway and they can pound sand. Something similar could be put in place for solar/wind installations.
I have seen conflicting claims about ham antennas.
If you have an overriding right to a ham antenna, you can threaten to put one up if they don't back down over something else. (To be clear, this would be a good thing.) If you already have one, you could threaten to expand it.
