The term "banana republic" refers to a country dominated by corporate interests, in which income disparity between rich and poor is extremely high, to the point that the middle class has just about disappeared, and aside from the fantastically wealthy few, practically everyone is dirt poor.
A Banana Republican is a Republican who wants to lower taxes for the rich, leading to increased income disparity and bringing the USA closer to banana republic status.
The GOP is full of Banana Republicans these days.