"Bat", of course, refers to members of the order chiroptera (with some contending that the "megachiroptera" of South America should be classified as primates), strange and wonderful animals which are beneficial to
humanity. Intelligent,
well-educated
liberals recognize bats as an asset, and seek to encourage them through environmental protection, including the building of bathouses on the outsides of their homes. The ignorant and superstitious hate and fear bats, and can think of no worse insult than to compare
people they also hate and fear (out of ignorance) to bats.
"Moon" refers to
Earth's primary natural sattelite, which
humans visited for a brief
period thanks to a massive liberal spending program. The scientific and technological benefits of the Apollo Project were immense, and would have been far greater if the program had not been killed by a right-wing administration that wanted to spend that money on a futile foreign war. Thus, the Moon is, like bats, symbolic of liberalism and all the benefits it brings to a culture, and naturally will be an object of hatred and fear to the Right.
Combine the
two and you get "Moonbat"; environmental good sense, scientific curiosity, prosperity for all and the triumph of knowledge over traditional superstition. In
short, all the things that enemies of civilization like Osama bin Laden and Pat Robertson hate most.