A Gypsy moth Republican, informally, is a politically pejorative term used by conservative Republicans to describe a moderate Republican serving in the U.S. House of Representatives who happens to represent a northeastern or midwestern urban area of the U.S. (an area that is also the habitat for the invasive Gypsy moth, an insect that damages trees and agriculture). Congressman Carl Pursell of Michigan was often described as the quintessential Gypsy Moth Republican in the 1980s.
The implication is that the Gypsy moth Republicans do damage to the Republican Party by siding occasionally with the more liberal Democratic Party.
Contrast this term with Boll Weevil Democrats (or Blue Dog Democrats), who are characterized as more moderate or conservative Democrats who occasionally side with the Republicans.