LORELAI: So, I think I’m in touch with the other side …
RORY: With Republicans?
The Republican Party in the US, founded in 1854 by anti-slavery activists, with an elephant as its symbol, for reasons nobody seems sure about. It shifted towards the right in the early twentieth century and is now a socially conservative party, tending to favour free market economics. It supports lower taxes, gun rights, restrictions on immigration, restrictions on abortion, restrictions on unions, and increased military spending. Since the 1850s it has been the main political rival to the Democratic Party, so when Lorelai says she is in touch with “the other side” (meaning the supernatural realm), Rory asks whether she means the other side of politics. Lorelai and Rory are Democrat supporters.
The Annotated Gilmore Girls 