Here are two versions of changing the gray color. In the first, I simply change the theme so that the gray area is white. In the second, I adjust the values in the RED and BLUE data frames and change the axis limits to have the color extend beyond the data.
ggplot(df,aes(x,y))+geom_point()+
geom_vline(xintercept=7.5,linetype="dashed") +
geom_area(aes(x=X,y=Y),data=RED,alpha=0.3,fill="red")+
geom_area(aes(x=X,y=Y),data=BLUE,alpha=0.3,fill="blue")+
theme_bw()
#Second method
RED <- data.frame(X=c(-1, 7.5), Y = 11)
BLUE <- data.frame(X=c(7.5, 11), Y = 11)
ggplot(df,aes(x,y))+geom_point()+
geom_vline(xintercept=7.5,linetype="dashed") +
geom_area(aes(x=X,y=Y),data=RED,alpha=0.3,fill="red")+
geom_area(aes(x=X,y=Y),data=BLUE,alpha=0.3,fill="blue")+
coord_cartesian(xlim = c(0,10), ylim = c(0,10))+
theme_bw()