"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.