Manually change order of y axis items on complicated stacked bar chart in ggplot2

I've been stuck on an issue and can't find a solution. I've tried many suggestions on Stack Overflow and elsewhere about manually ordering a stacked bar chart, since that should be a pretty simple fix, but those suggestions don't work with the huge complicated mess of code I plucked from many places. My only issue is y-axis item ordering.

I'm making a series of stacked bar charts, and ggplot2 changes the ordering of the items on the y-axis depending on which dataframe I am trying to plot. I'm trying to make 39 of these plots and want them to all have the same ordering. I think ggplot2 only wants to plot them in ascending order of their numeric mean or something, but I'd like all of the bar charts to first display the group "Bird Advocates" and then "Cat Advocates." (This is also the order they appear in my data frame, but that ordering is lost at the coord_flip() point in plotting.)

I think that taking the data frame through so many changes is why I can't just add something simple at the end or use the reorder() function. Adding things into aes() also doesn't work, since the stacked bar chart I'm creating seems to depend on those items being exactly a certain way.

Here's one of my data frames where ggplot2 is ordering my y-axis items incorrectly, plotting "Cat Advocates" before "Bird Advocates":

Group,Strongly Opposed,Opposed,Slightly Opposed,Neutral,Slightly Support,Support,Strongly Support
Bird Advocates,0.005473026,0.010946052,0.012509773,0.058639562,0.071149335,0.31118061,0.530101642
Cat Advocates,0.04491726,0.07013396,0.03624901,0.23719464,0.09141056,0.23404255,0.28605201

And here's all the code that takes that and turns it into a plot:

library(ggplot2)
library(reshape2)
library(plotly)

#Importing data from a .csv file
data <- read.csv("data.csv", header=TRUE)

data$s.Strongly.Opposed <- 0-data$Strongly.Opposed-data$Opposed-data$Slightly.Opposed-.5*data$Neutral
data$s.Opposed <- 0-data$Opposed-data$Slightly.Opposed-.5*data$Neutral
data$s.Slightly.Opposed <- 0-data$Slightly.Opposed-.5*data$Neutral
data$s.Neutral <- 0-.5*data$Neutral
data$s.Slightly.Support <- 0+.5*data$Neutral
data$s.Support <- 0+data$Slightly.Support+.5*data$Neutral
data$s.Strongly.Support <- 0+data$Support+data$Slightly.Support+.5*data$Neutral

#to percents
data[,2:15]<-data[,2:15]*100

#melting
mdfr <- melt(data, id=c("Group"))
mdfr<-cbind(mdfr[1:14,],mdfr[15:28,3])
colnames(mdfr)<-c("Group","variable","value","start")

#remove dot in level names
mylevels<-c("Strongly Opposed","Opposed","Slightly Opposed","Neutral","Slightly Support","Support","Strongly Support")
mdfr$variable<-droplevels(mdfr$variable)
levels(mdfr$variable)<-mylevels

pal<-c("#bd7523", "#e9aa61", "#f6d1a7", "#999999", "#c8cbc0", "#65806d", "#334e3b")

ggplot(data=mdfr) +
  geom_segment(aes(x = Group, y = start, xend = Group, yend = start+value, colour = variable,
                   text=paste("Group: ",Group,"<br>Percent: ",value,"%")), size = 5) +
  geom_hline(yintercept = 0, color =c("#646464")) +
  coord_flip() + 
  theme(legend.position="top") +
  theme(legend.key.width=unit(0.5,"cm")) +
  guides(col = guide_legend(ncol = 12)) + #has 7 real columns, using to adjust legend position 
  scale_color_manual("Response", labels = mylevels, values = pal, guide="legend") +
  theme(legend.title = element_blank()) +
  theme(axis.title.x = element_blank()) +
  theme(axis.title.y = element_blank()) +
  theme(axis.ticks = element_blank()) +
  theme(axis.text.x = element_blank()) +
  theme(legend.key = element_rect(fill = "white")) +
  scale_y_continuous(breaks=seq(-100,100,100), limits=c(-100,100)) +  
  theme(panel.background = element_rect(fill = "#ffffff"),
        panel.grid.major = element_line(colour = "#CBCBCB"))

The plot: